17Chapter 19Temperature91Chapter 15TemperatureMultiple Choice1.In order to understand the concept of temperature it is necessary to understanda.the zeroth law of thermodynamics.b.the first law of thermodynamics.c.the second law of thermodynamics.d.all of the above.e.only (b) and (c) above.2.In order for two objects to have the same temperature, they musta.be in thermal equilibrium.b.be in thermal contact with each other.c.have the same relative hotness or coldness when touched.d.have all of the properties listed above.e.have only properties (b) and (c) above.3.A pressure of 10 mm Hg is measured at the triple-point of water using a constant-volume gas thermometer, what will the pressure be (in mm Hg) at 50C?a.68.3b.1.8c.31.8d.11.8e.8.54.A pressure of 10 mm Hg is measured using a constant-volume gas thermometer at a temperature of 50C. What is the pressure (in mm Hg) at the zero-point temperature?a.31.8b.11.8c.8.5d.54.6e.68.35.A temperature difference of 5 K is equal toa.a difference of 9 on the Celsius scale.b.a difference of 9 on the Fahrenheit scale.c.a difference of 2.8 on the Rankine scale.d.a difference of .5 on the Fahrenheit scale.e.a difference of 2.8 on the Celsius scale.6.A thermometer registers a change in temperature of 100F. What change in temperature does this correspond to on the Kelvin Scale?a.453b.328c.180d.55.6e.24.57.Helium condenses into the liquid phase at approximately 4 K. What temperature, in degrees Fahrenheit, does this correspond to?a.182b.269c.118d.452e.4848.Two thermometers are calibrated, one in degrees Celsius and the other in degrees Fahrenheit. At what temperature (in kelvins) do their readings measure the same temperature?a.218.15b.233.15c.273.15d.40.15e.09.A child has a temperature of 104F. What is the temperature in degrees kelvin?a.40b.406c.401d.313e.34910.At what temperature is the Celsius scale reading equal to twice the Fahrenheit scale reading?a.12.3Fb.24.6Fc.12.3Cd.6.1Ce.20F11.A bridge is made with segments of concrete 50 m long. If the linear expansion coefficient is 12 106 (C)1, how much spacing (in cm) is needed to allow for expansion during an extreme temperature change of 150F?a.10b.2.5c.7.5d.5.0e.9.512.A building made with a steel structure is 650 m high on a winter day when the temperature is 0F. How much taller (in cm) is the building when it is 100F? (The linear expansion coefficient of steel is 11 106(C)1.)a.71b.36c.40d.46e.65

13.A gallon container is filled with gasoline. How many gallons are lost if the temperature increases by 25F? (The volume expansion of gasoline is (C)1.) (Neglect the change in volume of the container.)a.2.4 102b.1.3 102c.3.6 102d.4.8 102e.9.6 10214.An auditorium has dimensions 10 m 10 m 60 m. How many moles of air fill this volume at STP?a. 2.7 102b. 2.7 104c. 2.7 103d. 2.7 105e. 2.7 10615.An auditorium has a volume of 6 103 m3. How many molecules of air are needed to fill the auditorium at STP?a. 1.6 1029b. 1.6 1027c. 1.6 1025d. 1.6 1023e. 1.6 102016.One mole of an ideal gas is held at a constant pressure of 1 atm. Find the change in volume (in liters) if the temperature changes by 50C.a.1b.2c.3d.4e.517.One mole of an ideal gas is held at a constant volume of 1 liter. Find the change in pressure if the temperature increases by 50C.a.3 atmb.4 atmc.2 atmd.1 atme.5 atm18.One mole of an ideal gas has a temperature of 25C. If the volume is held constant and the pressure is doubled, the final temperature (in C) will bea.174b.596c.50d.323e.2519.A bicycle pump contains air at STP. As the tire is pumped up, the volume of air decreases by 50% with each stroke. What is the new pressure of air (in atm) in the chamber after the first stroke, assuming no temperature change?a.2b.1c.0.5d.0.1e.320.A helium-filled balloon has a volume of 1 m3. As it rises in the earths atmosphere, its volume expands. What will its new volume be (in m3) if its original temperature and pressure are 20C and 1 atm, and its final temperature and pressure are 40C and 0.1 atm?a.4b.6c.8d.10e.1.521.A bubble having a diameter of 1.00 cm is released from the bottom of a swimming pool where the depth is 5.00 m. What will the diameter of the bubble be when it reaches the surface? The temperature of the water at the surface is 20.0C, whereas it is 15.0C at the bottom. (The density of water is 1.00103kg/m3.)a.1.05b.1.15c.1.45d.1.65e.1.3522.A scuba diver has his lungs filled to half capacity (3 liters) when 10 m below the surface. If the diver holds his breath while quietly rising to the surface, what will the volume of the lungs be (in liters) at the surface? Assume the temperature is the same at all depths. (The density of water is 1.0103kg/m3.)a.5.9b.4.5c.6.4d.3.9e.3.123.Two identical containers, A and B, hold equal amounts of the same ideal gas at the same Po, Vo and To. The pressure of A then decreases by a half while its volume doubles; the pressure of B doubles while its volume decreases by a half. Which statement correctly describes the temperatures of the gases after the changes?a.TA = 0.5TB = To.b.TB = 0.5TA = To.c.TB = TA = To.d.TA = 2TB = To.e.TB = 2TA = To.24.Which of the following is not a possible thermometric property of a body?a.The change in length of a solid.b.the change in volume of a gas at constant pressure.c.The change in pressure of a gas at constant volume.d.The change in weight at constant pressure and volume.e.The change in electrical resistance of a conductor.25.A pebble size object and a bowling ball size probe from a spaceship land on a large asteroid that is far from any star. After a long period of time has passed, it is highly probable that the pebble and the probea.have each had the same change in temperature.b.have each had the same change in volume.c.are in thermal equilibrium with one another.d.are not in thermal equilibrium with one another.e.are in thermal equilibrium with one another, but are not at the same temperature.26.A temperature difference of 9 Celsius degrees is equal to a Fahrenheit temperature difference ofa.5 Fahrenheit degrees.b.9 Fahrenheit degrees.c.16 Fahrenheit degrees.d.37 Fahrenheit degrees.e.41 Fahrenheit degrees.27.Death Valley in California receives many German tourists. When you convert a summer temperature reading of 130F to the Celsius scale they use at home, you find that the Celsius temperature isa.26C.b.54C.c.72C.d.176Ce.327C.

28.A beaker is filled to the 500 ml mark with alcohol. What increase in volume (in ml) the beaker contain when the temperature changes from 5C to 30C? (Neglect the expansion of the beaker, evaporation of alcohol and absorption of water vapor by alcohol.) a.0.47b.0.93c.1.4d.1.7e.2.5

29.What is the change in area (in cm2) of a 60.0 cm by 150 cm automobile windshield when the temperature changes from 0C to 36.0C. The coefficient of linear expansion of glass is .a.1.62b.2.92c.3.24d.4.86e.5.83

30.A container with a one-liter capacity at 27C is filled with helium to a pressure of 2 atm. (1atm=.) How many moles of helium does it hold?a.0.040b.0.080c.0.45d.0.90e.1.031.Two bodies can be in thermal equilibrium with one another when they are at the same temperature even if theya.absorb different quantities of thermal energy from their surroundings in equal time intervals.b.have different masses.c.have different volumes.d.have any of the properties listed above.e.have any of the properties listed above and one of them is contact with a third body at a different temperature.32.Angela claims that she wears a cylindrical-shaped hollow gold bracelet because it expands less than a solid one with a change in temperature. Clarissa claims that a cylindrical-shaped solid gold bracelet expands less than a hollow one. Which one, if either, is correct?a.Angela, because the bracelet expands outward on its outer surface and inward on its inner surface.b.Clarissa, because the bracelet expands outward on its outer surface and inward on its inner surface.c.Angela, because the inner circumference does not change, but the outer circumference expands.d.Clarissa, because the inner circumference does not change, but the outer circumference expands.e.Neither, because both the inner and outer circumferences increase in length.33.A student has written the equation below to convert a temperature in degrees Fahrenheit into Kelvins. What is wrong with this equation?

a.The factor in front of should be .

b.The numerical factor should multiply .c.An additional 273.15 Kelvins must be added to the right side of the equation.d.All the corrections above are required.e.Only corrections (b) and (c) are required.34.Two moles of an ideal gas are placed in a container of adjustable volume. When measurements are madea.the pressure is inversely proportional to the volume at constant temperature.b.the temperature is directly proportional to the volume at constant pressure.c.the temperature is directly proportional to the pressure at constant volume.d.all the statements above are found to be correct.e.only statements (a) and (b) are found to be correct.

35.When the coefficient of linear expansion, , and the temperature change, , are large, a length of a solid substance expands in length to

a..

b.

c..

d..

e..

36.A square plate has an area of at 20.0 C. It will be used in a low temperature experiment at where it must have an area of . What area must be removed form the plate at 20.0 C for it to have the correct area at 10.0 K? (The coefficient of linear expansion is .)

a.

b.

c.

d.

e.37.Equal volumes of hydrogen and helium gas are at the same pressure. The gram molecular mass of helium is four times that of hydrogen. If the total mass of both gases is the same, the ratio of the temperature of helium (He) to that of hydrogen (H2) is

a..

b..c.1.d.2.e.4.38.Equal masses of hydrogen and helium gas are at the same temperature in vessels of equal volume. The gram molecular mass of helium is four times that of hydrogen. If the total mass of both gases is the same, the ratio of the pressure of helium (He) to that of hydrogen (H2) is

a..

b..c.1.d.2.e.4.

39.Steel blocks A and B, which have equal masses, are at and . Block C, with , is at . Blocks A and B are placed in contact, isolated, and allowed to come into equilibrium. Then they are placed in contact with block C. At that instant,

a..

b..

c..

d..

e..

Open-Ended Problems40.A gold ring has an inner diameter of 2.168 cm at a temperature of 15.0C. Determine its diameter at 100C. (GOLD = 1.42 105/C) 2.171cm41.Determine the change in length of a 20-m railroad track made of steel if the temperature is changed from 15C to +35C. (STEEL = 1.1 105/C ) 1.1cm42.At what Fahrenheit temperature are the Kelvin and Fahrenheit temperatures numerically equal? 574F=574K

43.Suppose the ends of a 30-m long steel beam are rigidly clamped at 0C to prevent expansion. The beam has a cross-sectional area of 30 cm2. What force against the clamps does the beam exert when it is heated to 40C? [, ]. 2.6*10(5)44.The pressure of a substance is directly proportional to its volume when the temperature is held constant and inversely proportional to its temperature when the volume is held constant. Is this substance an ideal gas? Explain why your answer is correct.

Chapter 16 The Kinetic Theory of Gases Multiple Choice 1. A container having a volume of 1.0 m3 holds 5.0 moles of helium gas at 50C. If the helium behaves like an ideal gas, the total energy of the system is a. 2.0 104 J. b. 2.5 104 J. c. 1.7 103 J. d. 1.5 103 J. e. 4.0 104 J. 2. A container having a volume of 1.0 m3 holds 5.0 moles of helium gas at 50C. If the helium behaves like an ideal gas, the average kinetic energy per molecule is a. 6.7 1020 J. b. 1.0 1021 J. c. 1.0 1020 J. d. 6.7 1021 J. e. 1.3 1020 J. 3. The average kinetic energy of a nitrogen molecule at room temperature (20C) is a. 2 1021 J. b. 4 1021 J. c. 6 1021 J. d. 8 1021 J. e. 1 1020 J. 4. The average translational speed of a nitrogen molecule at room temperature (20C) is approximately (in m/s) a. 100. b. 500. c. 300. d. 700. e. 200. 5. A box contains about 5.0 1021 hydrogen atoms at room temperature (21C). Determine the thermal energy of these atoms. a. 10 J b. 20 J c. 30 J d. 5.0 J e. 1.0 J 6. Five gas molecules are found to have speeds of 100, 200, 300, 400, and 500 m/s. The rms speed (in m/s) is a. 390. b. 300. c. 360. d. 330. e. 320. 7. Find the specific heat (in cal/mole K) of a gas kept at constant volume when it takes 1.0 104 J of heat to raise the temperature of 5.0 moles of the gas 200 K above the initial temperature.a. 7.5 b. 5.0 c. 2.4 d. 10 e. 20 8. The air in an automobile engine at 20C is compressed from an initial pressure of 1.0 atm and a volume of 200 cm3 to a volume of 20 cm3. Find the temperature if the air behaves like an ideal gas ( = 1.4) and the compression is adiabatic. a. 730C b. 460C c. 25C d. 50C e. 20C 9. During an adiabatic compression, a volume of air decreases to 1/4 its original size. Calculate its final pressure if its original pressure was 1 atm. (Assume the air behaves like an ideal gas with = 1.4.) a. 7.0 b. 5.6 c. 3.5 d. 2.2 e. 0.14 10. An ideal gas is allowed to expand adiabatically until its volume increases by 50%. By approximately what factor is the pressure reduced? ( = 5/3.)a. 1.5 b. 2.0 c. 2.5 d. 3.0 e. 3.5 11. When we say that the speed of sound is measured under adiabatic conditions we assume that a. the time associated with heat conduction is slow relative to the speed of the wave. b. no heat can flow between the system and its surroundings. c. the speed of the wave is directly proportional to the bulk modulus. d. the speed of the wave is proportional to the square root of the bulk modulus. e. air is an ideal gas. 12. Assume 3.0 moles of a diatomic gas has an internal energy of 10 kJ. Determine the temperature of the gas after it has reached equilibrium. a. 270 K b. 160 K c. 800 K d. 1550 K e. 400 K 13. Nitrogen gas is heated by a pulsed laser to 50 000 K. If the diameter of the nitrogen atoms is assumed to be 1.0 x1010 m, and the pressure is 1.0 atm, what is the mean free path? a. 1.5 104 m b. 1.5 107 m c. 1.5 1010 m d. 1.5 1014 m e. 1.5 102 m 14. Assume molecules have an average diameter of 3.00 1010 m. How many times larger is the mean free path than the diameter at STP? (Assume the pressure is 1.01105 N/m2 .) a. 500 b. 300 c. 700 d. 1000 e. 2500 15. The internal energy of n moles of an ideal gas depends on a. one state variable T. b. two state variables T and V. c. two state vartiables T and P. d. three state variables T, P and V. e. four variables R, T, P and V. 16. A molecule in a uniform ideal gas can collide with other molecules when their centers are equal to or less than a. one radius away from its center. b. one diameter away from its center. c. two diameters away from its center. d. twice the cube root of volume away from its center. e. 2 diameters away from its center. 17. The average molecular translational kinetic energy of a molecule in an ideal gas is 3a. kBT. 23b. RT. 25c. kBT. 25d. RT. 2n+3e. kBT, where n = number of internal degrees of freedom.

18. The relation PV = nRT holds for all ideal gases. The additional relation PV holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: means is proportional to.) PVAB a. Isotherm: P 1; Adiabat: P 1: A is both an isotherm and an adiabat.

VV1b. Isotherm: P; Adiabat: P : B is an isotherm, A is an adiabat. VV1c. Isotherm: P ; Adiabat: P : A is an isotherm, B is an adiabat. VV1d. Isotherm: P ; Adiabat: P: B is both an isotherm and an adiabat. VVe. I cannot answer this without additional information about the starting temperature. 19. Which statement below is NOT an assumption made in the molecular model of an ideal gas? a. The average separation between molecules is large compared with the dimensions of the molecules. b. The molecules undergo inelastic collisions with one another. c. The forces between molecules are short range. d. The molecules obey Newtons laws of motion. e. Any molecule can move in any direction with equal probability. 20. The theorem of equipartition of energy states that the energy each degree of freedom contributes to each molecule in the system (an ideal gas) is 1a. mv2 . 2 1b. k TB . 3 1c. 1k TB . 3 d. mv2. 4 3e. k TB . 221. The specific heat at constant volume at 0C of one mole of an ideal monatomic gas is 1a. R . 2b. R. 3c. R . 2d. 2R. 5e. R . 222. The specific heat at constant volume at 0C of one mole of an ideal diatomic gas is 1a. R . 2b. R. 3c. R . 2d. 2R. 5e. R . 223. The specific heat at constant pressure at 0C of one mole of an ideal monatomic gas is 1a. R . 2b. R. 3c. R . 2d. 2R. 5e. R . 224. When we consider a thin horizontal layer of the atmosphere, of thickness dy, of area A, with pressure P on the bottom, with an average mass m per molecule, and nV molecules per unit volume, the magnitude of the difference of the pressure at the top and bottom of the layer is given by dP = a. mgdy. b. mgnVdy. c. mgAdy. d. mgnVAdy. e. mgnVAPdy. 25. Burt states that the molecular model of an ideal gas assumes that the molecules of the gas do not collide with one another. Brooks states that it assumes that there is only one molecule moving back and forth between opposite walls in the container. Which one, if either, is correct? a. Burt, because the time interval between collisions with the same wall is 2dt = , where v, the velocity, is perpendicular to two opposite walls. vb. Brooks, because t will be greater if there is more than one molecule in the container. c. Both, because (a) and (b) are both correct. d. Both, because t , a time average over the components of velocity perpendicular to pairs of walls, is correct as long as the density is low and collisions are inelastic. e. Neither: t , a time average over the components of velocity perpendicular to pairs of walls, is correct as long as the density is low and collisions are elastic. 26. The temperature of a quantity of an ideal gas is a. one measure of its ability to transfer thermal energy to another body. b. proportional to the average molecular kinetic energy of the molecules. c. proportional to the internal energy of the gas. d. correctly described by all the statements above. e. correctly described only by (a) and (b) above. 27. Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal numbers of moles of gas. The gram-molecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion? a. The total internal energy of the hydrogen is the same as that of the helium. b. The total internal energy of the hydrogen is 1.4 times that of the helium. c. The total internal energy of the helium is 1.4 times that of the hydrogen. d. The total internal energy of the hydrogen is 1.67 times that of the helium. e. The total internal energy of the helium is 1.67 times that of the hydrogen. 28. Two tanks of gas, one of hydrogen, H2, and one of helium, He, contain equal masses of gas. The gram-molecular mass of He is twice that of H2. Both tanks of gas are at the same temperature, 293 K. Which statement(s) below is(are) correct when we ignore vibrational motion? a. The total internal energy of the hydrogen is the same as that of the helium. b. The total internal energy of the hydrogen is 167 times that of the helium. c. The total internal energy of the helium is 1.67 times that of the hydrogen. d. The total internal energy of the hydrogen is 3.33 times that of the helium. e. The total internal energy of the helium is 3.33 times that of the hydrogen. 29. One mole of hydrogen, one mole of nitrogen and one mole of oxygen are held in a 22.4 103 cm3 enclosed vessel at 20 C. The pressure in the vessel, in N/m2, is a. 109. b. 304. c. 326. d. 1.09 105. e. 3.26 105. 30. The root mean square speed of a gas molecule is greater than the average speed, because the former gives a greater weight to a. lighter molecules. b. heavier molecules. c. lower speeds. d. higher speeds. e. more probable speeds.

Chapter 17Electric FieldsMultiple Choice1. Each of two small non-conducting spheres is charged positively, the combined charge being 40 C. If each sphere is repelled from the other by a force having a magnitude of 2.0 N when the two spheres are 50 cm apart, determine the charge on the sphere having the smaller charge.a. 1.4 Cb. 1.1 Cc. 2.0 Cd. 3.3 Ce. 17 C2. A particle (charge = +40 C) is located on the x axis at the point x = 20 cm, and a second particle (charge = 50 C) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = 4.0 C) placed at the origin (x = 0)?a. 41 Nb. 16 Nc. 56 Nd. 35 Ne. 72 N3. In the figure, if Q = 30 C, q = 5.0 C, and d = 30 cm, what is the magnitude of the electrostatic force on q?d2d

Qq2Qa. 15 Nb. 23 Nc. zerod. 7.5 Ne. 38 N4. A charge of +80 C is placed on the x axis at x = 0. A second charge of 50 C is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 C placed on the x axis at x = 30 cm?a. 13 Nb. 77 Nc. 39 Nd. 25 Ne. 45 N5. Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 C at x = 0, +20 C at x = 40 cm, and 60 C at x = 60 cm, what is the magnitude of the electrostatic force on the +32-C charge?a. 84 Nb. 12 Nc. 36 Nd. 50 Ne. 48 N6. A particle (m = 50 g, q = 5.0 C) is released from rest when it is 50 cm from a second particle (Q = 20 C). Determine the magnitude of the initial acceleration of the 50-g particle.a. 54 m/ s2b. 90 m/ s2c. 72 m/ s2d. 65 m/ s2e. 36 m/ s27. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, Q, is placed at x = 3.0 m. If Q = 40 C, what is the magnitude of the electrostatic force on a 30-C charge placed at the origin?a. 7.2 Nb. 3.9 Nc. 1.5 Nd. 14 Ne. 8.1 N8. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, Q, is placed at x = 1.0 m. If Q = 60 C, what is the magnitude of the electrostatic force on a 40-C charge placed at the origin?a. 16 Nb. 27 Nc. 32 Nd. 11 Ne. 3.0 N9. A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = 1.0 m and another at x = +1.0 m. If Q = 40 C, what is the magnitude of the electrostatic force on the charge at x = +1.0 m?a. 29 Nb. 14 Nc. 11 Nd. 18 Ne. 7.0 N

10. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 36 nC in the figure, what is the magnitude of the total electric force on q?a. 5.0 Nb. 4.4 Nc. 3.8 Nd. 5.7 Ne. 0.60 N11. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 30 nC in the figure, what is the magnitude of the total electric force on q?ab

Q1Q2qa. 1.4 Nb. 1.0 Nc. 1.7 Nd. 2.0 Ne. 0.50 N12. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 40 nC in the figure, what is the magnitude of the total electric force on q?ab

qQ1Q2a. 1.8 Nb. 2.3 Nc. 2.7 Nd. 3.0 Ne. 4.2 N13. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 24 nC in the figure, what is the magnitude of the total electric force on q?qQ2Q1ba90

a. 2.7 Nb. 1.9 Nc. 2.3 Nd. 1.5 Ne. 0.52 N14. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 32 nC in the figure, what is the magnitude of the total electric force on q?qQ2Q1baa

a. 1.6 Nb. 1.3 Nc. 1.9 Nd. 2.2 Ne. 0.04 N15. If a = 3.0 mm, b = 4.0 mm, Q1 = 40 nC, Q2 = 80 nC, and q = 12 nC in the figure, what is the magnitude of the total electric force on q?Q1qba90

Q2a. 0.78 Nb. 0.68 Nc. 0.58 Nd. 0.88 Ne. 0.62 N16. A particle (charge = +50 C) is placed on the y axis at the point y = +40 cm, and a second particle (charge = 20 C) is placed at the origin (x = y = 0). What is the direction of the total electrostatic force on a third particle with respect to the +x-axis (charge = 5.0 C) placed on the x axis at the point x = +30 cm?a. 33b. 57c. 53d. 127e. 63

17. Three point charges, two positive and one negative, each having a magnitude of 20 C are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on the negative charge?a. 80 Nb. 40 Nc. 69 Nd. 57 Ne. 75 N18. Three point charges, two positive and one negative, each having a magnitude of 20 C are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on one of the positive charges?a. 69 Nb. 40 Nc. 80 Nd. 57 Ne. 20 N19. Identical point charges Q are placed at two of the vertices of an equilateral triangle(length of each side = 50 cm). A third charge, 2Q, is placed at the third vertex. If Q = 20 C, what is the magnitude of the electrostatic force on either of the positive charges?a. 76 Nb. 56 Nc. 39 Nd. 25 Ne. 29 N20. A point charge Q is placed at the origin. A second charge, 2Q, is placed on the x axis at x = 3.0 m. If Q = 50 C, what is the magnitude of the electrostatic force on a third point charge, Q, placed on the y axis at y = +4.0 m?a. 2.5 Nb. 3.0 Nc. 3.7 Nd. 4.4 Ne. 1.8 N21. Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m). If Q = 60 C, what is the magnitude of the electrostatic force on any one of the charges?a. 25 Nb. 19 Nc. 14 Nd. 22 Ne. 16 N

22. Identical point charges Q are placed at each of the four corners of a 3.0 m 4.0 m rectangle. If Q = 40 C, what is the magnitude of the electrostatic force on any one of the charges?a. 3.0 Nb. 2.4 Nc. 1.8 Nd. 3.7 Ne. 2.0 N23. A point charge (5.0 C) is placed on the x axis at x = 4.0 cm, and a second charge (+5.0 C) is placed on the x axis at x = 4.0 cm. What is the magnitude of the electric force on a third charge (+2.5 C) placed on the y axis at y = 3.0 cm?a. 90 Nb. 45 Nc. 54 Nd. 72 Ne. 36 N24. If Q = 25 C, q = 10 C, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q?qLL90

+QQa. 28 Nb. 22 Nc. 20 Nd. 14 Ne. 10 N6Chapter 23Chapter 2323

2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved.25. Q = 20 C and L = 60 cm, what is the magnitude of the electrostatic force on any one of the charges shown?LLLLQ+Q+QQ

a. 25 Nb. 19 Nc. 15 Nd. 9.1 Ne. 14 N26. If a = 60 cm, b = 80 cm, Q = 4.0 nC, and q = 1.5 nC, what is the magnitude of the electric field at point P shown?baaqbQP

a. 68 N/ Cb. 72 N/ Cc. 77 N/ Cd. 82 N/ Ce. 120 N/ C27. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 4.0 nC, what is the magnitude of the electric field at point P shown?baqQP90

28. a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 6.0 nC, what is the magnitude of the electric field at point P in the figure?abQq90P

a. 65 N/ Cb. 55 N/ Cc. 60 N/ Cd. 52 N/ Ce. 67 N/ C29. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P?aabQqP90

a. 71 N/ Cb. 56 N/ Cc. 60 N/ Cd. 53 N/ Ce. 67 N/ C30. Two particles, having oppositely signed charges of +12 nC, are placed at two of the vertices of an equilateral triangle (length of each side = 2.0 m). What is the magnitude of the electric field at the third vertex of the triangle?A. 27B. 36C. 45D. 5431. Q = 16 nC, a = 3.0 m, and b = 4.0 m, what is the magnitude of the electric field at point P shown?QQQbaP90

a. 33 N/ Cb. 31 N/ Cc. 24 N/ Cd. 19 N/ Ce. 13 N/ C32. If Q = 80 nC, a = 3.0 m, and b = 4.0 m in the figure, what is the magnitude of the electric field at point P?2Q2QQPbaa90

a. 45 N/ Cb. 70 N/ Cc. 29 N/ Cd. 47 N/ Ce. 92 N/ C33. A +2.0-nC point charge is placed at one corner of a square (1.5 m on a side), and a 3.0-nC charge is placed on a corner diagonally away from the first charge. What is the magnitude of the electric field at either of the two unoccupied corners?a. 20 N/ Cb. 14 N/ Cc. 4.0 N/ Cd. 12 N/ Ce. 8.0 N/ C34. A +15-nC point charge is placed on the x axis at x = 1.5 m, and a 20-nC charge is placed on the y axis at y = 2.0m. What is the magnitude of the electric field at the origin? c

35. A +20-nC point charge is placed on the x axis at x = 2.0 m, and a 25-nC point charge is placed on the y axis at y = 3.0 m. What is the direction of the electric field at the origin?a. 209b. 61c. 29d. 241e. 15136. A charge Q is placed on the x axis at x = +4.0 m. A second charge q is located at the origin. If Q = +75 nC and q = 8.0 nC, what is the magnitude of the electric field on the y axis at y = +3.0 m?a. 19 N/ Cb. 23 N/ Cc. 32 N/ Cd. 35 N/ Ce. 21 N/ C37. A 40-C charge is positioned on the x axis at x = 4.0 cm. To produce a net electric field of zero at the origin where should a 60-C charge be placed?a. 5.3 cmb. 5.7 cmc. 4.9 cmd. 6.0 cme. +6.0 cm38. A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m.a. 30 N/ Cb. 15 N/ Cc. 48 N/ Cd. 90 N/ Ce. 60 N/ C39. A charge (uniform linear density = 9.0 nC/ m) is distributed along the x axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.a. 81 N/ Cb. 74 N/ Cc. 61 N/ Cd. 88 N/ Ce. 20 N/ C40. A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies?a. 81 N/ Cb. 61 N/ Cc. 71 N/ Cd. 51 N/ Ce. 25 N/ C41. Charge of uniform density 4.0 nC/ m is distributed along the x axis from x = 2.0 m to x = +3.0 m. What is the magnitude of the electric field at the point x = +5.0 m on the x axis?a. 16 N/ Cb. 13 N/ Cc. 19 N/ Cd. 26 N/ Ce. 5.0 N/ C42. A uniformly charged rod (length = 2.0 m, charge per unit length = 5.0 nC/ m) is bent to form one quadrant of a circle. What is the magnitude of the electric field at the center of the circle?a. 62 N/ Cb. 56 N/ Cc. 50 N/ Cd. 44 N/ Ce. 25 N/ C43. A uniformly charged rod (length = 2.0 m, charge per unit length = 3.0 nC/ m) is bent to form a semicircle. What is the magnitude of the electric field at the center of the circle?a. 64 N/ Cb. 133 N/ Cc. 48 N/ Cd. 85 N/ Ce. 34 N/ C45. A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC. What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?a. 40 N/ Cb. 45 N/ Cc. 24 N/ Cd. 90 N/ Ce. 36 N/ C46. A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m. What is the magnitude of the electric field at the origin?a. 18 N/ Cb. 50 N/ Cc. 30 N/ Cd. 15 N/ Ce. 90 N/ C47. A linear charge of uniform density equal to 8.0 nC/ m is distributed along the x axis from x = 2.0 m to x = 3.0 m. What is the magnitude of the electric field at the point x = 6.0 m on the x axis?a. 60 N/ Cb. 10 N/ Cc. 26 N/ Cd. 15 N/ Ce. 45 N/ C48. A uniform linear charge of 2.0 nC/ m is distributed along the x axis from x = 0 to x = 3 m. What is the x component of the electric field at y = 2 m on the y axis?a. 5.0 N/ Cb. 4.0 N/ Cc. 5.7 N/ Cd. 6.2 N/ Ce. 9.0 N/ C49. A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.5 N/ C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vx = 80 m/ s, vy = vz = 0, what is the speed of the particle at t = 2.0 s?a. 40 m/ sb. 20 m/ sc. 60 m/ sd. 80 m/ se. 180 m/ sChapter 2313x16Chapter 23xChapter 2330x

2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved.50. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.5 N/ C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vy = 50 m/ s, vx = vz = 0, what is the speed of the particle at t = 2.0 s?a. 81 m/ sb. 72 m/ sc. 64 m/ sd. 89 m/ se. 25 m/ s51. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 5.5 N/ C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = 0 and vx = 50 m/ s, vy = vz = 0, what is the distance from the origin to the particle at t = 2.0 s?a. 60 mb. 28 mc. 44 md. 12 me. 88 m52. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.3 N/ C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = 0 and vz = 20 m/ s, vx = vy = 0, what is the distance from the origin to the particle at t = 2.0 s?a. 60 mb. 54 mc. 69 md. 78 me. 3.2 m53. An electron enters a region of uniform electric field (E = 50 N/ C) with an initial velocity of 40 km/ s directed the same as the electric field. What is the speed of the electron 1.5 ns after entering this region?a. 53 km/ sb. 27 km/ sc. 18 km/ sd. 62 km/ se. 42 km/ s54. A particle (q = 3.0 mC, m = 20 g) has a speed of 20 m/ s when it enters a region where the electric field has a constant magnitude of 80 N/ C and a direction which is the same as the velocity of the particle. What is the speed of the particle 3.0 s after it enters this region?a. 68 m/ sb. 44 m/ sc. 56 m/ sd. 80 m/ se. 36 m/ s55. A particle (q = 4.0 mC, m = 50 g) has a velocity of 25 m/ s in the positive x direction when it first enters a region where the electric field is uniform (60 N/ C in the positive y direction). What is the speed of the particle 5.0 s after it enters this region?a. 49 m/ sb. 35 m/ sc. 32 m/ sd. 44 m/ se. 24 m/ s56. A charge of 50 C is placed on the y axis at y = 3.0 cm and a 77-C charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin?a. 1.2 1020 m/ s2b. 1.5 1020 m/ s2c. 1.0 1020 m/ s2d. 1.8 1020 m/ s2e. 2.0 1020 m/ s257. The velocity of a particle (m = 10 mg, q = 4.0 C) at t = 0 is 20 m/ s in the positive x direction. If the particle moves in a uniform electric field of 20 N/ C in the positive x direction, what is the particle's speed at t = 5.0 s?a. 60 m/ sb. 20 m/ sc. 45 m/ sd. 40 m/ se. 70 m/ s58. A particle (m = 20 mg, q = 5.0 C) moves in a uniform electric field of 60 N/ C in the positive x direction. At t = 0, the particle is moving 25 m/ s in the positive x direction and is passing through the origin. How far is the particle from the origin at t = 2.0 s?a. 80 mb. 20 mc. 58 md. 10 me. 30 m59. A particle (m = 20 mg, q = 5.0 C) moves in a uniform electric field of 60 N/ C in the positive x direction. At t = 0, the particle is moving 30 m/ s in the positive x direction and is passing through the origin. Determine the maximum distance beyond x = 0 the particle travels in the positive x direction.a. 25 mb. 20 mc. 15 md. 30 me. 60 m

66. Electric field lines in the space surrounding a charge distribution show:a. the directions of the forces that exist in space at all times.b. only the directions in which static charges would accelerate when at points on those linesc. only the directions in which moving charges would accelerate when at points on those lines.d. the directions in which either static or moving charges would accelerate when passing through points on those lines.e. the paths static or moving charges would take.67. When a positive charge q is placed in the field created by two other charges Q1 and Q2, each a distance a away from q, the acceleration of q is:a. in the direction of the charge Q1 or Q2 of smaller magnitude.b. in the direction of the charge Q1 or Q2 of greater magnitude.c. in the direction of the negative charge if Q1 and Q2 are of opposite sign.d. in the direction of the positive charge if Q1 and Q2 are of opposite sign.e. in a direction determined by the vector sum of the electric fields of Q1 and Q2.68. Two charged particles, Q1 and Q2, are a distance r apart. Q2 = 5Q1. Compare the forces they exert on each other. F1 is the force Q2 exerts on Q1. F2 is the force Q1 exerts on Q2. a. F2 = 5F1.b. F2 = 5F1.c. F2 = F1.d. F2 = F1.e. 5F2 = F1.

69. Rubber rods charged by rubbing with cat fur repel each other. Glass rods charged by rubbing with silk repel each other. A rubber rod and a glass rod charged respectively as above attract each other. A possible explanation is that:a. Any two rubber rods charged this way have opposite charges on them.b. Any two glass rods charged this way have opposite charges on them.c. A rubber rod and a glass rod charged this way have opposite charges on them.d. All rubber rods always have an excess of positive charge on them.e. All glass rods always have an excess of negative charge on them.

70. Enrico says that positive charge is created when you rub a glass rod with silk, and that negative charge is simply the absence of positive charge. Rosetta says that negative charge is created and that positive charge is the absence of positive charge. (She has heard that Ben Franklin should have reversed the signs he associated with the charges.) Which one, if either, is correct?1) Enrico, because there really is only one kind of charge.2) Rosetta, because there really is only one kind of charge.3) Neither: although no charge is present originally, both types of charge are created through friction.4) Both: only one type of charge is created by friction at any one time.5) Neither: both negative and positive charge are present simultaneously in all solid materials on Earth.

Chapter 18Gauss' LawMultiple Choice1. Two charges of 15 pC and 40 pC are inside a cube with sides that are of 0.40-m length. Determine the net electric flux through the surface of the cube.a. +2.8 N m2/ Cb. 1.1 N m2/ Cc. +1.1 N m2/ Cd. 2.8 N m2/ Ce. 0.47 N m2/ C2. The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equal to 5.0 N m2/ C. Determine the net charge within the cylinder.a. 62 pCb. 53 pCc. 44 pCd. 71 pCe. 16 pC3. Charges q and Q are placed on the x axis at x = 0 and x = 2.0 m, respectively. If q = 40 pC and Q = +30 pC, determine the net flux through a spherical surface (radius = 1.0 m) centered on the origin.a. 9.6 N m2/ Cb. 6.8 N m2/ Cc. 8.5 N m2/ Cd. 4.5 N m2/ Ce. 1.1 N m2/ C4. A uniform linear charge density of 4.0 nC/ m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin. Determine the electric flux through this surface.a. 68 N m2/ Cb. 62 N m2/ Cc. 45 N m2/ Cd. 79 N m2/ Ce. 23 N m2/ C5. A uniform charge density of 500 nC/ m3 is distributed throughout a spherical volume (radius = 16 cm). Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.a. 7.1 N m2/ Cb. 3.6 N m2/ Cc. 12 N m2/ Cd. 19 N m2/ Ce. 970 N m2/ C6. A point charge +Q is located on the x axis at x = a, and a second point charge Q is located on the x axis at x = a. A Gaussian surface with radius r = 2a is centered at the origin. The flux through this Gaussian surface isa. zero because the negative flux over one hemisphere is equal to the positive flux over the other.b. greater than zero.c. zero because at every point on the surface the electric field has no component perpendicular to the surface.d. zero because the electric field is zero at every point on the surface.e. none of the above7. The xy plane is "painted" with a uniform surface charge density which is equal to 40 nC/ m2. Consider a spherical surface with a 4.0-cm radius that has a point in the xy plane as its center. What is the electric flux through that part of the spherical surface for which z > 0?a. 14 N m2/ Cb. 11 N m2/ Cc. 17 N m2/ Cd. 20 N m2/ Ce. 23 N m2/ C8. A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a uniform charge density of 1.3 C/ m3. Determine the electric flux through a spherical surface (radius = 2.0 cm) which has a point on the axis of the cylinder as its center.a. 5.7 N m2/ Cb. 4.9 N m2/ Cc. 6.4 N m2/ Cd. 7.2 N m2/ Ce. 15 N m2/ C9. Charge of uniform surface density (4.0 nC/ m2) is distributed on a spherical surface (radius = 2.0 cm). What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm?a. 2.8 N m2/ Cb. 1.7 N m2/ Cc. 2.3 N m2/ Cd. 4.0 N m2/ Ce. 9.1 N m2/ C10. A charge of uniform volume density (40 nC/ m3) fills a cube with 8.0-cm edges. What is the total electric flux through the surface of this cube?a. 2.9 N m2/ Cb. 2.0 N m2/ Cc. 2.6 N m2/ Cd. 2.3 N m2/ Ce. 1.8 N m2/ C11. A charge of 0.80 nC is placed at the center of a cube that measures 4.0 m along each edge. What is the electric flux through one face of the cube?a. 90 N m2/ Cb. 15 N m2/ Cc. 45 N m2/ Cd. 23 N m2/ Ce. 64 N m2/ C12. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface?a. R2Eb. 4R2E/ 3c. 2R2E/ 3d. R2E/ 2e. R2E/ 313. The electric field in the region of space shown is given by E = (8i + 2yj) N/ C where y is in m. What is the magnitude of the electric flux through the top face of the cube shown?xyz3m3m3m2mTop Facea. 90 N m2/C

b. 6.0 N m2/ Cc. 54 N m2/ Cd. 12 N m2/ Ce. 126 N m2/ C14. Charge of uniform surface density (0.20 nC/ m2) is distributed over the entire xy plane. Determine the magnitude of the electric field at any point having z = 2.0 m.a. 17 N/ Cb. 11 N/ Cc. 23 N/ Cd. 28 N/ Ce. 40 N/ C15. Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/ m2 and 0.60 nC/ m2. What is the magnitude of the electric field at a point between the two surfaces?a. 34 N/ Cb. 23 N/ Cc. 45 N/ Cd. 17 N/ Ce. 90 N/ C16. Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has a charge density of +60 pC/ m2, and the other carries a charge density of 80 pC/ m2. What is the magnitude of the electric field at any point not on either surface?a. 1.1 N/ Cb. 5.6 N/ Cc. 7.9 N/ Cd. 3.8 N/ Ce. 4.0 N/ C17. Charge of a uniform density (8.0 nC/ m2) is distributed over the entire xy plane. A charge of uniform density (5.0 nC/ m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 1.0 m.a. 730 N/ Cb. 450 N/ Cc. 280 N/ Cd. 170 N/ Ce. 340 N/ C18. Charge of a uniform density (8.0 nC/ m2) is distributed over the entire xy plane. A charge of uniform density (3.0 nC/ m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m.a. 0.79 kN/ Cb. 0.17 kN/ Cc. 0.62 kN/ Cd. 0.34 kN/ Ce. 0.28 kN/ C19. Charge of a uniform density (8.0 nC/ m2) is distributed over the entire xy plane. A charge of uniform density (5.0 nC/ m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 1.0 m.a. 0.45 kN/ Cb. 0.17 kN/ Cc. 0.28 kN/ Cd. 0.73 kN/ Ce. 0.62 kN/ C20. Charge of uniform density (0.30 nC/ m2) is distributed over the xy plane, and charge of uniform density (0.40 nC/ m2) is distributed over the yz plane. What is the magnitude of the resulting electric field at any point not in either of the two charged planes?a. 40 N/ Cb. 34 N/ Cc. 28 N/ Cd. 46 N/ Ce. 6.0 N/ C21. A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/ m3) distributed throughout its column. Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder.a. 25 N/ Cb. 20 N/ Cc. 14 N/ Cd. 31 N/ Ce. 34 N/ C22. A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/ m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the axis of the cylinder.a. 20 N/ Cb. 27 N/ Cc. 16 N/ Cd. 12 N/ Ce. 54 N/ C23. Each 2.0-m length of a long cylinder (radius = 4.0 mm) has a charge of 4.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point 5.0 mm from the axis of the cylinder?a. 9.9 kN/ Cb. 8.1 kN/ Cc. 9.0 kN/ Cd. 7.2 kN/ Ce. 18 kN/ C24. A long nonconducting cylinder (radius = 6.0 mm) has a nonuniform volume charge density given by r2, where = 6.0 mC/ m5 and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis?a. 1.4 N/ Cb. 1.6 N/ Cc. 1.8 N/ Cd. 2.0 N/ Ce. 5.4 N/ C25. Charge is uniformly distributed along the entire x axis. If each 20-cm length of the x axis carries 2.0 nC of charge, what is the magnitude of the electric field at the point, y = 2.0 m, on the y axis?a. 45 N/ Cb. 90 N/ Cc. 18 N/ Cd. 36 N/ Ce. 180 N/ C26. A long cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If the magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/ C, how much charge is distributed on a 2.0-m length of the charged cylindrical surface?a. 0.38 nCb. 0.76 nCc. 0.19 nCd. 0.57 nCe. 0.98 nC27. Charge of uniform linear density (4.0 nC/ m) is distributed along the entire x axis. Determine the magnitude of the electric field on the y axis at y = 2.5 m.a. 36 N/ Cb. 29 N/ Cc. 43 N/ Cd. 50 N/ Ce. 58 N/ C28. Charge of uniform density (80 nC/ m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii, 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis.a. 7.9 N/ Cb. 9.0 N/ Cc. 5.9 N/ Cd. 6.8 N/ Ce. 18 N/ C

2Chapter 24Chapter 2441

2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved.29. Charge of uniform density (80 nC/ m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii, 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 4.0 mm from the symmetry axis.a. 7.9 N/ Cb. 10 N/ Cc. 9.0 N/ Cd. 8.9 N/ Ce. 17 N/ C30. Charge of uniform density (20 nC/ m2) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of 12 nC/ m2. Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces.a. 2.3 kN/ Cb. 1.1 kN/ Cc. 1.7 kN/ Cd. 3.4 kN/ Ce. 4.5 kN/ C31. Charge of uniform density (20 nC/ m2) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of 12 nC/ m2. Determine the magnitude of the electric field at a point 4.0 cm from the symmetry axis of the two surfaces.a. 0.45 kN/ Cb. 1.0 kN/ Cc. 0.73 kN/ Cd. 0.56 kN/ Ce. 2.3 kN/ C32. Charge of uniform density (40 pC/ m2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/ m2. What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?a. 3.8 N/ Cb. 4.1 N/ Cc. 3.5 N/ Cd. 3.2 N/ Ce. 0.28 N/ C33. A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/ m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the center of the sphere.22 N/ C49 N/ C31 N/ C87 N/ C26 N/ C34. A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of 8.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?a. 1.8 105 N/ Cb. 9.0 104 N/ Cc. 3.6 105 N/ Cd. 2.7 105 N/ Ce. 7.2 105 N/ C35. A sphere (volume = 12 cm3) is filled with a nonconducting material which carries a charge of 2.0 pC distributed uniformly throughout the volume. What is the magnitude of the electric field 1.0 cm from the center of the sphere?a. 24 N/ Cb. 180 N/ Cc. 63 N/ Cd. 120 N/ Ce. 197 N/ C36. A charge of 5.0 pC is uniformly distributed throughout the volume between concentric spherical surfaces having radii of 1.0 cm and 3.0 cm. What is the magnitude of the electric field 2.0 cm from the center of the surfaces?a. 33 N/ Cb. 113 N/ Cc. 30 N/ Cd. 450 N/ Ce. 47 N/ C37. A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of 2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.a. 30 N/ Cb. 50 N/ Cc. 40 N/ Cd. 20 N/ Ce. 70 N/ C38. A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of 3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.14 N/ C11 N/ C22 N/ C18 N/ C40 N/ C39. A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm), and a charge of 3.0 pC is spread uniformly upon this surface. Determine the magnitude of the electric field 1.0 cm from the point charge.a. 0.72 kN/ Cb. 0.45 kN/ Cc. 0.63 kN/ Cd. 0.90 kN/ Ce. 0.18 kN/ C40. Charge of uniform density (40 pC/ m2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/ m2. What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces?a. 1.1 N/ Cb. 4.5 N/ Cc. 1.4 N/ Cd. 5.6 N/ Ce. 0.50 N/ C41. A surface charge of uniform density 3.0 nC/ m2 is placed on a spherical surface which has a radius of 2.0 mm. A uniform surface charge (density = 10 nC/ m2) is placed on a concentric spherical surface (radius = 8.0 mm). What is the magnitude of the electric field 5.0 mm from the center of these surfaces?a. 63 N/ Cb. 54 N/ Cc. 72 N/ Cd. 45 N/ Ce. 36 N/ C42. A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm, outer radius = 4.0 cm) conducting sphere which has a net charge of 4.0 pC. Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge.a. 35 N/ Cb. 25 N/ Cc. 30 N/ Cd. 20 N/ Ce. 10 N/ C43. The axis of a long hollow metallic cylinder (inner radius = 1.0 cm, outer radius = 2.0 cm) coincides with a long wire. The wire has a linear charge density of 8.0 pC/ m, and the cylinder has a net charge per unit length of 4.0 pC/ m. Determine the magnitude of the electric field 3.0 cm from the axis.5.4 N/ C 7.2 N/ C 4.3 N/ C 3.6 N/ C2.4 N/ CChapter 24310Chapter 24Chapter 2445

a.b.c.d.e. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved.44. A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/ m2. Determine the magnitude of the electric field 3.0 mm from the axis.a. 18 N/ Cb. 23 N/ Cc. 30 N/ Cd. 15 N/ Ce. 60 N/ C45. If the electric field just outside a thin conducting sheet is equal to 1.5 N/ C, determine the surface charge density on the conductor.a. 53 pC/ m2b. 27 pC/ m2c. 35 pC/ m2d. 13 pC/ m2e. 6.6 pC/ m246. The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/ C. What is the charge density on the surface of the cylinder?a. 2.7 nC/ m2b. 1.8 nC/ m2c. 3.5 nC/ m2d. 4.4 nC/ m2e. 0.90 nC/ m247. A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow spherical conductor (inner radius = 3.0 cm, outer radius = 4.0 cm) which has a total charge of 3.0 pC. What is the magnitude of the electric field 2.0 cm from the center of these conductors?a. 23 N/ Cb. zeroc. 45 N/ Cd. 90 N/ Ce. 110 N/ C48. A long cylindrical conductor (radius = 1.0 mm) carries a charge density of 4.0 pC/ m and is inside a coaxial, hollow, cylindrical conductor (inner radius = 3.0 mm, outer radius = 4.0 mm) that has a total charge of 8.0 pC/ m. What is the magnitude of the electric field 2.0 mm from the axis of these conductors?a. 24 N/ Cb. 18 N/ Cc. zerod. 36 N/ Ce. 226 N/ C49. The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a magnitude of 500 N/ C and is directed outward. An unknown charge Q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 N/ C. What is the magnitude of the charge Q?a. 1.5 nCb. 1.8 nCc. 1.3 nCd. 1.1 nCe. 2.7 nC50. The axis of a long hollow metallic cylinder (inner radius = 1.0 cm, outer radius = 2.0 cm) coincides with a long wire. The wire has a linear charge density of +8.0 nC/ m, and the cylinder has a net charge per unit length of +4.0 nC/ m. Determine the surface charge density on the outer surface of the cylinder.a. 95 nC/ m2b. 64 nC/ m2c. 48 nC/ m2d. 38 nC/ m2e. 32 nC/ m251. A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 2.0 cm) which has a net charge of 4.0 nC. Determine the resulting charge density on the inner surface of the conducting sphere.a. +4.8 C/ m2b. 4.8 C/ m2c. 9.5 C/ m2d. +9.5 C/ m2e. 8.0 C/ m252. An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station. Which statement is correct?a. The astronaut must abandon the chamber immediately to avoid being electrocuted.b. The astronaut will be safe only if she is wearing a spacesuit made of non-conducting materials.c. The astronaut does not need to worry: the charge will remain on the outside surface.d. The astronaut must abandon the chamber if the electric field on the outside surface becomes greater than the breakdown field of air.e. The astronaut must abandon the chamber immediately because the electric field inside the chamber is non-uniform.53. A small metal sphere is suspended from the conducting cover of a conducting metal ice bucket by a non-conducting thread. The sphere is given a negative charge before the cover is placed on the bucket. The bucket is tilted by means of a non-conducting material so that the charged sphere touches the inside of the bucket. Which statement is correct?a. The negative charge remains on the metal sphere.b. The negative charge spreads over the outside surface of the bucket and cover.c. The negative charge spreads over the inside surface of the bucket and cover.d. The negative charge spreads equally over the inside and outside surfaces of the bucket and cover.e. The negative charge spreads equally over the sphere and the inside and outside surfaces of the bucket and cover.54. A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown. Where is the induced charge density greatest in magnitude and what is its sign?DCABq

a. A; negative.b. A; positive.c. B; negative.d. B; positivee. C; negative55. A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground. The outside of the sphere is then grounded as shown. A is the inner surface and B is the outer surface. Which statement is correct?ABq

a. The charge on A is q; that on B is +q.b. The charge on B is q; that on A is +q.qc. The charge is on A and on B. 2d. There is no charge on either A or B.e. The charge on A is q; there is no charge on B.56. An uncharged metal sphere is placed on an insulating puck on a frictionless table. A rod with a charge q is brought close to the sphere, but does not touch it. As the rod is brought in, the spherea. remains at rest.b. moves toward the rod.c. moves away from the rod.d. moves perpendicular to the velocity vector of the rod.e. moves upward off the puck.57. Three originally uncharged infinite parallel planes are arranged as shown. Then the upper plate has surface charge density placed on it while the lower plate receives surface charge density . The net charge induced on the center plate is+

a. 0.b. / 2.c. +/ 2.d. .

Chapter 19Electric PotentialMultiple Choice1. A charged particle (q = 8.0 mC), which moves in a region where the only force acting on the particle is an electric force, is released from rest at point A. At point B kinetic energy of the particle is equal to 4.8 J. What is the electric potential difference VB VA?a. 0.60 kVb. +0.60 kVc. +0.80 kVd. 0.80 kVe. +0.48 kV2. A particle (charge = 50 C) moves in a region where the only force on it is an electric force.As the particle moves 25 cm from point A to point B, its kinetic energy increases by 1.5 mJ. Determine the electric potential difference, V B VA.a. 50 Vb. 40 Vc. 30 Vd. 60 Ve. +15 V3. Points A [at (2, 3) m] and B [at (5, 7) m] are in a region where electric field is uniform and given by E = (4i + 3j) N/C. What is the potential difference VA VB?a. 33 Vb. 27 Vc. 30 Vd. 24 Ve. 11 V4. A particle (charge = +2.0 mC) moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point A. The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A. Determine the kinetic energy of the particle as it moves through point B.a. 3.0 Jb. 2.0 Jc. 5.0 Jd. 8.0 Je. 10.0 J5. A particle (mass 6.7 1027 kg, charge 3.2 1019 C) moves along the positive x axis with a speed of 4.8 105 m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 2.0 m into the field. What is the magnitude of the electric field?a. 2.0 kN/Cb. 1.5 kN/Cc. 1.2 kN/Cd. 3.5 kN/Ce. 2.4 kN/C6. A proton (mass = 1.67 1027 kg, charge = 1.60 1019 C) moves from point A to point B under the influence of an electrostatic force only. At point A the proton moves with a speed of 50 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference VB VA.a. +20 Vb. 20 Vc. 27 Vd. +27 Ve. 40 V7. A proton (mass = 1.67 1027 kg, charge = 1.60 1019 C) moves from point A to point B under the influence of an electrostatic force only. At point A the proton moves with a speed of 60 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference VB VA.a. +15 Vb. 15 Vc. 33 Vd. +33 Ve. 20 V8. What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV?a. 1.1 106 m/sb. 9.8 105 m/sc. 8.8 105 m/sd. 1.2 106 m/se. 6.2 105 m/s9. An electron (m = 9.1 1031 kg, q = 1.6 1019 C) starts from rest at point A and has a speed of 5.0 106 m/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference VA VB.a. 71 Vb. +71 Vc. 26 Vd. +26 Ve. 140 V10. A proton (m = 1.7 1027 kg, q = +1.6 1019 C) starts from rest at point A and has a speed of 40 km/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference VB VA.a. +8.5 Vb. 8.5 Vc. 4.8 Vd. +4.8 Ve. 17 V11. A particle (m = 2.0 g, q = 5.0 nC) has a speed of 30 m/s at point A and moves (with only electric forces acting on it) to point B where its speed is 80 m/s. Determine the electric potential difference VA VB.a. 2.2 kVb. +1.1 kVc. 1.1 kVd. +2.2 kVe. 1.3 kV12. A particle (m = 8.0 g, q = +6.0 nC) has a speed of 80 m/s at point A and moves to point B where the electric potential is 2.0 kV greater than at point A. What is the particle's kinetic energy at point B? Only electric forces act on the particle during this motion. a. 14 Jb. 38 Jc. 10 Jd. 34 Je. 40 J13. An alpha particle (m = 6.7 1027 kg, q = +3.2 1019 C) has a speed of 20 km/s at point A and moves to point B where it momentarily stops. Only electric forces act on the particle during this motion. Determine the electric potential difference VA VB.a. +4.2 Vb. 4.2 Vc. 9.4 Vd. +9.4 Ve. 8.4 V14. Points A [at (3, 6) m] and B [at (8, 3) m] are in a region where the electric field is uniform and given by E = 12i N/C. What is the electric potential difference VA VB?a. +60 Vb. 60 Vc. +80 Vd. 80 Ve. +50 V15. If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = 3.0 nC in the figure, what is the potential difference VA VB?a b a q A B Qa. +60 Vb. +72 Vc. +84 Vd. +96 Ve. +48 V16. Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity) and an electric field of 36i N/C at point P. Determine the work required of an external agent to move a 3.0-C charge from infinity to point P (without any net change in the kinetic energy of the particle) along the x axis.a. 21 mJb. 18 mJc. 24 mJd. 27 mJe. 12 mJ17. Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = 2.0 nC, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, VA VB?baa90BAQq90

a. 8.4 Vb. 6.0 Vc. 7.2 Vd. 4.8 Ve. 0 V18. Three charged particles lie on the x axis. There are a 70-nC charge at x = 7, a 100-nC charge at x = 3, and a 50-nC charge at x = 10. What is the electric potential (relative to zero at infinity) at the origin? (All distances are in meters.)a. 0.17 kVb. +0.44 kVc. +0.83 kVd. 0.26 kVe. 0.48 kV

4Chapter 23Chapter 5454

2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved.19. Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis, a 80-nC charge at x = 4 m on the x axis, and a 70-nc charge at y = 6 m on the y axis. What is the electric potential (relative to a zero at infinity) at the point x = 8 m on the x axis?a. +81 Vb. +48 Vc. +5.8 Vd. 72 Ve. 18 V20. Point charges of equal magnitudes (25 nC) and opposite signs are placed on (diagonally) opposite corners of a 60-cm 80-cm rectangle. If point A is the corner of this rectangle nearest the positive charge and point B is located at the intersection of the diagonals of the rectangle, determine the potential difference, VB VA.a. 47 Vb. +94 Vc. zerod. 94 Ve. +47 V21. Identical 2.0-C charges are located on the vertices of a square with sides that are 2.0 m in length. Determine the electric potential (relative to zero at infinity) at the center of the square.a. 38 kVb. 51 kVc. 76 kVd. 64 kVe. 13 kV22. A +4.0-C charge is placed on the x axis at x = +3.0 m, and a 2.0-C charge is located on the y axis at y = 1.0 m. Point A is on the y axis at y = +4.0 m. Determine the electric potential at point A (relative to zero at the origin).a. 6.0 kVb. 8.4 kVc. 9.6 kVd. 4.8 kVe. 3.6 kV23. Identical 4.0-C charges are placed on the y axis at y = 4.0 m. Point A is on the x axis at x = +3.0 m. Determine the electric potential of point A (relative to zero at the origin).a. 4.5 kVb. 2.7 kVc. 1.8 kVd. 3.6 kV24. Four identical point charges (+6.0 nC) are placed at the corners of a rectangle which measures 6.0 m 8.0 m. If the electric potential is taken to be zero at infinity, what is the potential at the geometric center of this rectangle?a. 58 Vb. 63 Vc. 43 Vd. 84 Ve. 11 V25. Three identical point charges (+2.0 nC) are placed at the corners of an equilateral triangle with sides of 2.0-m length. If the electric potential is taken to be zero at infinity, what is the potential at the midpoint of any one of the sides of the triangle?a. 16 Vb. 10 Vc. 70 Vd. 46 Ve. 44 V26. A particle (charge = Q) is kept in a fixed position at a position at a point P, and a second particle (charge = q) is released from rest when it is a distance R from P. If Q = +2.0 mC, q = 1.5 mC, and R = 30 cm, what is the kinetic energy of the moving particle after it has moved a distance of 10cm?a. 60 kJb. 45 kJc. 75 kJd. 90 kJe. 230 kJ27. A particle (charge = q) is released from rest when it is a distance of 3.0 m from a point charge Q, which is held at a fixed position. If Q = 50 C and q = 36 C, what is the kinetic energy of the particle after it has traveled 1.0 m?a. 3.3 Jb. 3.0 Jc. 2.7 Jd. 3.6 Je. 14 J28. Particle A (mass = m, charge = Q) and B (mass = m, charge = 5 Q) are released from rest with the distance between them equal to 1.0 m. If Q = 12 C, what is the kinetic energy of particle B at the instant when the particles are 3.0 m apart?a. 8.6 Jb. 3.8 Jc. 6.0 J d. 2.2 Je. 4.3 J29. A particle (charge = 40 C) moves directly toward a second parti cle (charge = 80 C) which is held in a fixed position. At an instant when the distance between the two particles is 2.0 m, the kinetic energy of the moving particle is 16 J. Determine the distance separating the two particles when the moving particle is momentarily stopped.a. 0.75 mb. 0.84 mc. 0.95 md. 0.68 me. 0.56 m30. A particle (charge 7.5 C) is released from rest at a point on the x axis, x = 10 cm. It begins to move due to the presence of a 2.0-C charge which remains fixed at the origin. What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m?a. 3.0 Jb. 1.8 Jc. 2.4 Jd. 1.2 Je. 1.4 J31. A particle (charge = 5.0 C) is released from rest at a point x = 10 cm. If a 5.0-C charge is held fixed at the origin, what is the kinetic energy of the particle after it has moved 90 cm?a. 1.6 Jb. 2.0 Jc. 2.4 Jd. 1.2 Je. 1.8 J32. A 60-C charge is held fixed at the origin and a 20-C charge is held fixed on the x axis at a point x = 1.0 m. If a 10-C charge is released from rest at a point x = 40 cm, what is its kinetic energy the instant it passes the point x = 70 cm?a. 9.8 Jb. 7.8 Jc. 8.8 Jd. 6.9 Je. 2.8 J33. Two identical particles, each with a mass of 2.0 mg and a charge of 25 nC, are released simultaneously from rest when the two are 4.0 cm apart. What is the speed of either particle at the instant when the two are separated by 10 cm?a. 7.3 m/sb. 9.8 m/sc. 9.2 m/sd. 6.5 m/se. 4.6 m/sChapter 2538Chapter 2358

c.d.e. 2000 by Harcourt College Publishers. All rights reserved.

2000 by Harcourt College Publishers. All rights reserved.34. Two particles, each having a mass of 3.0 mg and having equal but opposite charges of magnitude 5.0 nC, are released simultaneously from rest when the two are 5.0 cm apart. What is the speed of either particle at the instant when the two are separated by 2.0 cm? a.2.1 m/sb. 1.5 m/sc. 1.8 m/sd. 2.4 m/se. 3.2 m/s35. Two identical particles, each with a mass of 4.5 mg and a charge of 30 nC, are moving directly toward each other with equal speeds of 4.0 m/s at an instant when the distance separating the two is equal to 25 cm. What minimum separation distance will the two achieve?a. 9.8 cmb. 12 cmc. 7.8 cmd. 15 cme. 20 cm36. Two particles, each having a mass of 3.0 mg and having equal but opposite charges of magnitude of 6.0 nC, are released simultaneously from rest when they are a very large distance apart. What distance separates the two at the instant when each has a speed of 5.0 m/s?a. 4.3 mmb. 8.6 mmc. 7.3 mmd. 5.6 mme. 2.2 mm37. A particle (q = +5.0 C) is released from rest when it is 2.0 m from a charged particle which is held at rest. After the positively charged particle has moved 1.0 m toward the fixed particle, it has a kinetic energy of 50 mJ. What is the charge on the fixed particle? a. 2.2 Cb. +6.7 Cc. 2.7 Cd. +8.0 Ce. 1.1 C38. Four identical point charges (+4.0 C) are placed at the corners of a square which has 20-cm sides. How much work is required to assemble this charge arrangement starting with each of the charges a very large distance from either of the other charges?a. +2.9 Jb. +3.9 Jc. +2.2 Jd. +4.3 Je. +1.9 J39. Identical 8.0-C point charges are positioned on the x axis at x = 1.0 m and released from rest simultaneously. What is the kinetic energy of either of the charges after it has moved 2.0 m?a. 84 mJb. 54 mJc. 96 mJd. 63 mJe. 48 mJ40. Two particles with equal masses and oppositely signed charges are placed on the x axis at x = 4.0 m and released from rest at t = 0. If the magnitude of each of the charges is 4.0 C, what is the kinetic energy of either particle after it has moved 2.0 m?a. 3.5 mJb. 5.1 mJc. 6.9 mJd. 9.0 mJe. 3.0 mJ41. Through what potential difference must an electron (starting from rest) be accelerated if it is to achieve a speed of 3.0 107 m/s?a. 5.8 kVb. 2.6 kVc. 7.1 kVd. 8.6 kVe. 5.1 kV42. Identical point charges (+50 C) are placed at the corners of a square with sides of 2.0-m length. How much external energy is required to bring a fifth identical charge from infinity to the geometric center of the square?a. 41 Jb. 16 Jc. 64 Jd. 10 Je. 80 J43. A charge of +3.0 C is distributed uniformly along the circumference of a circle with a radius of 20 cm. How much external energy is required to bring a charge of 25C from infinity to the center of the circle?a. 5.4 Jb. 3.4 Jc. 4.3 Jd. 2.7 Je. 6.8 J44. Identical point charges (+20 C) are placed at the corners of an equilateral triangle with sides of 2.0-m length. How much external energy is required to bring a charge of 45 C from infinity to the midpoint of one side of the triangle?a. 26 Jb. 16 Jc. 23 Jd. 21 Je. 12 J45. Identical point charges (+30 C) are placed at the corners of a rectangle (4.0 m 6.0 m). How much external energy is required to bring a charge of 55 C from infinity to the midpoint of one of the 6.0-m lengths of the rectangle?a. 22 Jb. 16 Jc. 13 Jd. 19 Je. 8.0 J46. A charge per unit length given by (x) = bx, where b = 12 nC/m2, is distributed along the x axis from x = +9.0 cm to x = +16 cm. If the electric potential at infinity is taken to be zero, what is the electric potential at a point P on the y axis at y = 12 cm?a. 5.4 Vb. 7.2 Vc. 9.0 Vd. 9.9 Ve. 16 V47. A charge Q is uniformly distributed along the x axis from x = a to x = b. If Q = 45 nC, a = 3.0 m, and b = 2.0 m, what is the electric potential (relative to zero at infinity) at the point, x = 8.0 m, on the x axis?a. 71 Vb. 60 Vc. 49 Vd. 82 Ve. 150 V48. Charge of uniform density (3.5 nC/m) is distributed along the circular arc shown. Determine the electric potential (relative to zero at infinity) at point P.60RRP+++++++++++

a. 61 Vb. 42 Vc. 52 Vd. 33 Ve. 22 V49. A charge of uniform density (0.80 nC/m) is distributed along the x axis from the origin to the point x = 10 cm. What is the electric potential (relative to zero at infinity) at a point, x = 18 cm, on the x axis?a. 7.1 Vb. 5.8 Vc. 9.0 Vd. 13 Ve. 16 V50. A charge of 20 nC is distributed uniformly along the x axis from x = 2 m to x = +2.0 m. What is the electric potential (relative to zero at infinity) at the point x = 5.0 m on the x axis?a. 57 Vb. 48 Vc. 38 Vd. 67 Ve. 100 V51. Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m to x = 5.0 m. What is the electric potential (relative to zero at infinity) at the origin (x = 0)?a. 91 Vb. 99 Vc. 82 Vd. 74 Ve. 140 V52. A linear charge of nonuniform density = bx, where b = 2.1 nC/m2, is distributed along the x axis from x = 2.0 m to x = 3.0 m. Determine the electric potential (relative to zero at infinity) of the point y = 4.0 m on the y axis.a. 36 Vb. 95 Vc. 10 Vd. 17 Ve. 15 V53. A nonuniform linear charge distribution given by (x) = bx, where b is a constant, is distributed along the x axis from x = 0 to x = +L. If b = 40 nC/m2 and L = 0.20 m, what is the electric potential (relative to a potential of zero at infinity) at the point, y = 2L, on the y axis?a. 19 Vb. 17 Vc. 21 Vd. 23 Ve. 14 V57. A rod (length = 2.0 m) is uniformly charged and has a total charge of 5.0 nC. What is the electric potential (relative to zero at infinity) at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?a. 22 Vb. 19 Vc. 16 Vd. 25 Ve. 12 V61. Two large parallel conducting plates are 8.0 cm apart and carry equal but opposite charges on their facing surfaces. The magnitude of the surface charge density on either of the facing surfaces is 2.0 nC/m2. Determine the magnitude of the electric potential difference between the plates.a. 36 Vb. 27 Vc. 18 Vd. 45 Ve. 16 V62. Charge of density 3.0 C/m fills a long cylindrical region having a 2.0-cm radius. If point A is 1.0 cm from the symmetry-axis and point B is 2.0 cm from the symmetry-axis, what is the potential difference VA VB?a. 25 mVb. +42 mVc. 42 mVd. +25 mVe. +20 mV63. An infinite charged sheet has a surface charge density of 10 nC/m2. Determine the potential difference between equipotential surfaces (on the same side of the sheet charge) that are separated by a distance of 7.0 mm.a. 5.9 Vb. 4.0 Vc. 7.9 Vd. 9.9 Ve. 13 V64. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on its surface. If point A is located at the center of the sphere and point B is 15 cm from the center, what is the magnitude of the electric potential difference between these two points?a. 23 Vb. 30 Vc. 15 Vd. 45 Ve. 60 V65. Charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a.2.7 Vb. 2.0 Vc. 2.4 Vd. 1.7 Ve. 3.4 V66. Charge of uniform density 90 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 2.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a. 1.9 Vb. 1.4 Vc. 2.2 Vd. 2.8 Ve. 4.0 V67. A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3. What is the magnitude of the potential difference between the center and a point 4.0 cm away?a. 12 Vb. 6.8 Vc. 3.0 Vd. 4.7 Ve. 2.2 V68. A charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cm radius. Point A is 1.0 cm from the center of the conductor and point B is 5.0 cm from the center of the conductor. Determine the electric potential difference VA VB.a. +1.8 Vb. +29 Vc. +27 Vd. +7.2 Ve. +9.0 V69. A 2.0-nC charge is uniformly distributed over the surface of a solid spherical(radius = 2.0 cm) conductor which is concentric with a hollow spherical conductor (radii = 3.0 cm and 5.0 cm) which has a net charge of 3.0 nC. Determine the electric potential of the outer conductor relative to the inner conductor.a. +0.30 kVb. 0.30 kVc. 0.45 kVd. +0.45 kVe. 0.15 kV70. Two flat conductors are placed with their inner faces separated by 6.0 mm. If the surface charge density on one of the inner faces is 40 pC/m2, what is the magnitude of the electric potential differences between the two conductors?a. 36 mVb. 18 mVc. 32 mVd. 27 mVe. 14 mV71. The electric field in a region of space is given by Ex = (3.0x) N/C, Ey = Ez = 0, where x is in m. Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m. Determine the potential difference VB VA.a. 24 Vb. +24 Vc. 18 Vd. +30 Ve. 6.0 V72. Equipotentials are lines along whicha. the electric field is constant in magnitude and direction.b. the electric charge is constant in magnitude and direction.c. a charge moving at constant speed requires that the maximum amount of work be done against electrical forces.d. a charge may be moved at constant speed without work against electrical forces.e. charges move by themselves.73. When a charged particle is moved along an electric field line,a. the electric field does no work on the charge.b. the electrical potential energy of the charge does not change.c. the electrical potential energy of the charge undergoes the maximum change in magnitude.d. the voltage changes, but there is no change in electrical potential energy.e. the electrical potential energy undergoes the maximum change, but there is no change in voltage.74. When a positive chanrge is released and moves along an electric field line, it moves to a position ofa. lower potential and lower potential energy.b. lower potential and higher potential energy.c. higher potential and lower potential energy.d. higher potential and higher potential energy.e. greater magnitude of the electric field.75. When a negative charge is released and moves along an electric field line, it moves to a position ofa. lower potential and lower potential energy.b. lower potential and higher potential energy.c. higher potential and lower potential energy.d. higher potential and higher potential energy.e. decreasing magnitude of the electric field.76. A charge is placed on a spherical conductor of radius r1. This sphere is then connected to a distant sphere of radius r2 (not equal to r1) by a conducting wire. After the charges on the spheres are in equilibrium,a. the electric fields at the surfaces of the two spheres are equal.b. the amount of charge on each sphere is q/2.c. both spheres are at the same potential.d. the potentials are in the ratio V2 = q2 .V1q1e. the potentials are in the ratio V2 = r2 .V1r177. The electric potential inside a charged solid spherical conductor in equilibrium:a. is always zero.b. is constant and equal to its value at the surface.c. decreases from its value at the surface to a value of zero at the center.d. increases from its value at the surface to a value at the center that is a multiple of the potential at the surface.e. is equal to the charge passing through the surface per unit time divided by the resistance.78. Which statement is always correct when applied to a charge distribution located in a finite region of space?a. Electric potential is always zero at infinity.b. Electric potential is always zero at the origin.c. Electric potential is always zero at a boundary surface to a charge distribution.d. Electric potential is always infinite at a boundary surface to a charge distribution.e. The location where electric potential is zero may be chosen arbitrarily.79. Which of the following represents the equipotential lines of a dipole?

ABCDE84.Can the lines in the figure below be equipotential lines?

a. No, because there are sharp corners.b. No, because they are isolated lines.c. Yes, because any lines within a charge distribution are equipotential lines.d. Yes, they might be boundary lines of the two surfaces of a conductor.e. It is not possible to say without further information.

Chapter 20Capacitance and DielectricsMultiple Choice1. If C = 12 pF, determine the equivalent capacitance for the combination shown.CCC2C

a. 48 pFb. 12 pFc. 24 pFd. 6.0 pFe. 59 pF2. If C = 15 mF, determine the equivalent capacitance for the combination shown.C2CCC

a. 20 mFb. 16 mFc. 12 mFd. 24 mFe. 75 mF3. If C = 12 nF, determine the equivalent capacitance for the combination shown.2CCC3C

a. 34 nFb. 17 nFc. 51 nFd. 68 nFe. 21 nF4. If C = 45 F, determine the equivalent capacitance for the combination shown.C2CC2C

a. 36 Fb. 32 Fc. 34 Fd. 30 Fe. 38 F5. If C = 50 nF, determine the equivalent capacitance for the combination shown.3CC2CC

a. 29 nFb. 0.19 Fc. 34 nFd. 0.23 Fe. 75 nF6. If C = 10 F, what is the equivalent capacitance for the combination shown?8.0 F6.0 FC

a. 7.5 Fb. 6.5 Fc. 7.0 Fd. 5.8 Fe. 13 F7. What is the equivalent capacitance of the combination shown?12 F24 F20 F12 F

a. 29 Fb. 10 Fc. 40 Fd. 25 Fe. 6.0 F8. What is the equivalent capacitance of the combination shown? 30F 30F20 F10 F

a. 20 Fb. 90 Fc. 22 Fd. 4.6 Fe. 67 F9. If C = 45 F, determine the equivalent capacitance for the combination shown.2C3CC6C

a. 28 Fb. 36 Fc. 52 Fd. 44 Fe. 23 F10. If C = 24 F, determine the equivalent capacitance for the combination shown.2CC2C2C2C

a. 20 Fb. 36 Fc. 16 Fd. 45 Fe. 27 F11. In the figure, if C1 = 15 F, C2 = 10 F, C3 = 20 F, and V0 = 18 V, determine the energy stored in C2.0.72 mJ+V0C2C3C1

a. 0.32 mJb. 0.50 mJc. 0.18 mJd. 1.60 mJ12. In the figure, if C1 = 5.0 F, C2 = 15 F, C3 = 30 F, V0 = 24 V, what is the total energy stored in the three capacitors?C2C3C1+V0

a. 4.3 mJb. 5.9 mJc. 7.7 mJd. 9.7 mJe. 1.3 mJ

4Chapter 26Chapter 2672

2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved.13. = 10 F, C2 = 12 F, C3 = 15 F, and V0 = 70 V, determine the energy stored in C1.+V0C1C2C3

a. 6.5 mJb. 5.1 mJc. 3.9 mJd. 8.0 mJe. 9.8 mJ14. In the figure, if C1 = 20 F, C2 = 10 F, C3 = 14 F, C4 = 30 F, and V0 = 45 V, determine the energy stored by C4.C1C4+V0C2C3

a. 3.8 mJb. 2.7 mJc. 3.2 mJd. 2.2 mJe. 8.1 mJ15. In the figure, if C1 = 20 F, C2 = 10 F,C3 = 30 F, and V0 = 18 V, determine the charge stored by C1.C1+V0C2C3

a. 0.37 mCb. 0.24 mCc. 0.32 mCd. 0.40 mCe. 0.50 mC16. = 50 F, C2 = 30 F, C3 = 36 F, C4 = 12 F, and V0 = 30 V, what is the total energy stored by C3?C4+V0C3C2C1

a. 6.3 mJb. 25 mJc. 57 mJd. 1.6 mJe. 14 mJ17. In the figure, if Va Vb = 22V, how much energy is stored in the 50-F capacitor?50 F25 F25 Fab

a. 0.78 mJb. 0.58 mJc. 0.68 mJd. 0.48 mJe. 0.22 mJ18. What is the total energy stored in the group of capacitors shown if the charge on the 30-F capacitor is 0.90 mC?30 F20 F15 F

a. 29 mJb. 61 mJc. 21 mJd. 66 mJe. 32 mJ19. = 5.0 F, C2 = 15 F, C3 = 30 F, and V0 = 24 V, what is the potential difference across C2?C2C3C1+V0

a. 21 Vb. 19 Vc. 16 Vd. 24 Ve. 8.0 V20. What total energy is stored in the group of capacitors shown if the potential difference Vab is equal to 50 V?50 F20 F10 Fab

a. 48 mJb. 27 mJc. 37 mJd. 19 mJe. 10 mJ21. Determine the energy stored in the 60-F capacitor shown.+50 V40 F60 F25 F

a. 2.4 mJb. 3.0 mJc. 3.6 mJd. 4.3 mJe. 6.0 mJChapter 265In the figure, if C18Chapter 26In the figure, if C1Chapter 2676In the figure, if C1

2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved. 2000 by Harcourt College Publishers. All rights reserved.22. Determine the energy stored in the 40-F capacitor shown.+50 V40 F60 F25 F

a. 2.4 mJb. 1.6 mJc. 2.0 mJd. 2.9 mJe. 4.0 mJ23. If VA VB = 50 V, how much energy is stored in the 36-F capacitor shown?36 F72 F54 FAB

a. 50 mJb. 28 mJc. 13 mJd. 8.9 mJe. 17 mJ24. If VA VB = 50 V, how much energy is stored in the 54-F capacitor shown?36 F72 F54 FAB

a. 50 mJb. 13 mJc. 28 mJd. 8.9 mJe. 17 mJ25. If a 3.0-F capacitor charged to 40 V and a 5.0-F capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other, what is the final charge on the 3.0-F capacitor?a. 11 Cb. 15 Cc. 19 Cd. 26 Ce. 79 C26. A 6.0-F capacitor charged to 50 V and a 4.0-F capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected. What is the total energy stored in the 6.0-F capacitor at equilibrium?a. 6.1 mJb. 5.7 mJc. 6.6 mJd. 7.0 mJe. 3.8 mJ27. A 25-F capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected. The final potential difference across the 25-F capacitor is 36 V. What is the value of the capacitance of C?a. 43 Fb. 29 Fc. 22 Fd. 58 Fe. 63 F28. A 15-F capacitor charged to 60 V and a 20-F capacitor charged to 10 V are connected to each other, with the positive plate of each connected to the negative plate of the other. What fraction of the total energy initially stored in these two capacitors is lost as a result of this connection?a. 0.50b. 0.75c. 0.33d. 0.25e. 029. A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other. What is the final charge on the 6.0-mF capacitor?a. 20 mCb. 8.0 mCc. 10 mCd. 12 mCe. 230 mC30. A charge of 80 C on a certain capacitor causes a potential difference of 16 V across its plates. How much energy is stored in this capacitor when the potential difference across its plates is 42 V?a. 1.0 mJb. 4.4 mJc. 3.2 mJd. 1.4 mJe. 1.7 mJ31. A 15-F capacitor and a 30-F capacitor are connected in series, and this combination is charged to a potential difference of 50 V. What is the resulting charge on the 30-F capacitor?a. 0.70 mCb. 0.80 mCc. 0.50 mCd. 0.60 mCe. 0.40 mC32. A 15-F capacitor and a 25-F capacitor are connected in parallel, and this combination is charged to a potential difference of 60 V. How much energy is then stored in this capacitor combination?a. 50 mJb. 18 mJc. 32 mJd. 72 mJe. 45 mJ33. A 20-F capacitor charged to 2.0 kV and a 40-F capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 20-F capacitor after the two are so connected?a. 53 mCb. 27 mCc. 40 mCd. 80 mCe. 39 mC34. A 15-F capacitor is charged to 40 V and then connected across an initially uncharged 25-F capacitor. What is the final potential difference across the 25-F capacitor?a. 12 Vb. 18 Vc. 15 Vd. 21 Ve. 24 V35. A 30-F capacitor is charged to 40 V and then connected across an initially uncharged 20-F capacitor. What is the final potential difference across the 30-F capacitor?a. 15 Vb. 24 Vc. 18 Vd. 21 Ve. 40 V36. A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60-F capacitor. If the final potential difference across the 60-F capacitor is 40 V, determine C.a. 49 Fb. 32 Fc. 40 Fd. 90 Fe. 16 F37. A 30-F capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C. If the final potential difference across the 30-F capacitor is 20 V, determine C.a. 60 Fb. 75 Fc. 45 Fd. 90 Fe. 24 F38. A 30-F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-F capacitor. If the final potential difference across the 10-F capacitor is 20 V, determine V0.a. 13 Vb. 27 Vc. 20 Vd. 29 Ve. 60 V39. A parallel plate capacitor of capacitance Co has plates of area A with separation d between them. When it is connected to a battery of voltage Vo, it has charge of magnitude Qo on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference betwen them are:a. Qo, Vob. Qo, Voc. Qo, Vod. Qo, 2Voe. 2Qo, 2Vo40. A parallel plate capacitor of capacitance Co has plates of area A with separation d between them. When it is connected to a battery of voltage Vo, it has charge of magnitude Qo on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the new capacitance and the potential difference betwen the plates are:a. Co, Vob. 2 Co, Voc. Co, Vod. Co, 2Voe. 2Co, 2Vo41. A parallel plate capacitor of capacitance Co has plates of area A with separation d between them. When it is connected to a battery of voltage Vo, it has charge of magnitude Qoon its plates. The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference betwen them are:a. Qo, Vob. 2 Qo, Voc. Qo, Vod. 2Qo, Voe. 2Qo, 2Vo42. A parallel plate capacitor of capacitance Co has plates of area A with separation d between them. When it is connected to a battery of voltage Vo, it has charge of magnitude Qo on its plates. The plates are pulled apart to a separation 2d while the capcitor remains connected to the battery. After the plates are 2d apart, the capacitance of the capacitor and the magnitude of the charge on the plates are:a. Co, Qob. 2 Co, Qoc. Co, Qod. 2Co, Qoe. 2Co, 2Qo43. A parallel plate capacitor of capacitance Co has plates of area A with separation d between them. When it is connected to a battery of voltage Vo, it has charge of magnitude Qoon its plates. While it is connected to the battery the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the potential difference betwen them are:a. Qo, Vob. Qo, Voc. Qo, Vod. 3Qo, Voe. 3Qo, 3Vo44. A parallel plate capacitor of capacitance Co has plates of area A with separation d between them. When it is connected to a battery of voltage Vo, it has charge of magnitude Qo on its plates. While it is connected to the battery, the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitude of the charge on the plates and the new capacitance are:a. Qo, Cob. Qo, Coc. Qo, Cod. 3Qo, Coe. 3Qo, 3Co

Chapter 21 Current and Resistance Multiple Choice 1. A rod of 2.0-m length and a square (2.0 mm 2.0 mm) cross section is made of a material with a resistivity of 6.0 108 m. If a potential difference of 0.50 V is placed across the ends of the rod, at what rate is heat generated in the rod? a. 3.0 W b. 5.3 W c. 8.3 W d. 1.3 W e. 17 W 2. An electric device, which heats water by immersing a resistance wire in the water, generates 50 cal of heat per second when an electric potential difference of 12 V is placed acros