Physics 1) Two small spheres, each with mass m = 5.0 g and charge q, are suspended from a point by threads of length L = 0.30 m. What is the charge on each sphere if the threads make an angle ϴ = 20° with the vertical? A) 7.9 10 –7 C B) 2.9 10 –7 C C) 7.5 10 –2 C D) 6.3 10 –13 C E) 1.8 10 –7 C 2) Charges q 1 and q 2 exert repulsive forces of 10 N on each other. What is the repulsive force when their separation is decreased so that their final separation is 80% of their initial separation? A) 16 N B) 12 N C) 10 N D) 8.0 N E) 6.4 N 3) Two positive charges (+8.0 mC and +2.0 mC) are separated by 300 m. A third charge is placed at distance r from the +8.0 mC charge in such a way that the resultant electric force on the third charge due to the other two charges is zero. The distance r is A) 0.25 km B) 0.20 km C) 0.15 km D) 0.13 km E) 0.10 km 4) Point charges of 4.0 × 10 –8 C and –2.0 × 10 –8 C are placed 12 cm apart. A third point charge of 3.0 × 10 –8 C halfway between the first two point charges experiences a force of magnitude A) 4.5 × 10 –3 N B) 2.0 × 10 –3 N C) 1.5 × 10 –3 N D) zero E) 5.0 ×10 –3 N 5) A charge 2Q is located at the origin while a second charge –Q is located at x = a. Where a third charge should be placed so that the net force on the charge is zero? Harshana Perera(B.Sc(Phy),BIT,SCJP)2014 R Kit Turn Over
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Physics
1) Two small spheres, each with mass m = 5.0 g and charge q, are suspended from a point by threads of length L = 0.30 m. What is the charge on each sphere if the threads make an angle ϴ = 20° with the vertical?
A) 7.9 10–7 C B) 2.9 10–7 CC) 7.5 10–2 C D) 6.3 10–13 CE) 1.8 10–7 C
2) Charges q1 and q2 exert repulsive forces of 10 N on each other. What is the repulsive force when their separation is decreased so that their final separation is 80% of their initial separation?
A) 16 N B) 12 N C) 10 N D) 8.0 N E) 6.4 N
3) Two positive charges (+8.0 mC and +2.0 mC) are separated by 300 m. A third charge is placed at distance r from the +8.0 mC charge in such a way that the resultant electric force on the third charge due to the other two charges is zero. The distance r is
A) 0.25 km B) 0.20 km C) 0.15 km D) 0.13 km E) 0.10 km
4) Point charges of 4.0 × 10–8 C and –2.0 × 10–8 C are placed 12 cm apart. A third point charge of 3.0 × 10–8 C halfway between the first two point charges experiences a force of magnitude
A) 4.5 × 10–3 N B) 2.0 × 10–3 N C) 1.5 × 10–3 N D) zero E) 5.0 ×10–3N
5) A charge 2Q is located at the origin while a second charge –Q is located at x = a. Where a third charge should be placed so that the net force on the charge is zero?
6) Three charges are located at 100-m intervals along a horizontal line: a charge of –3.0 C on the left, 2.0 C in the middle, and 1.0 C on the right. What is the electric field on the horizontal line halfway between the –3.0 C and 2.0 C charges?
A) 2.2 × 107 N/C to the left B) 1.8 × 107 N/C to the right C) 1.8 × 107 N/C to the leftD) 3.2 × 106 N/C to the right E) 4.0 × 106 N/C to the lef
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7) If all the charges are 15 cm from the origin (the crossing point of the vertical and horizontal lines) in the above figure and Q = +3.0 μC, then calculate the magnitude of the net force on a charge of +Q placed at the origin.
A) 22.8 NB) 10.2 NC) 26.0 ND) 187 NE) None of the above
8) Three charges, each of Q = 3.2 × 10–19 C, are arranged at three of the corners of a 20-nm square as shown. The magnitude of the electric field at D, the fourth corner of the square, is approximately
9) The electric field at point A is zero. What is charge Q1?
A) +32 μC B) –32 μC C) The field cannot be zero at A for any value of Q1.
D) +16 μC E) –16 μC
10) Two charges Q1 and Q2 are a distance d apart. If the electric field is zero at a distance of 3d/4 from Q1 (towards Q2), then what is the relation between Q1 and Q2?
A) Q1 = Q2 /9 B) Q1 = 9Q2 C) Q1 = Q2 D) Q1 = 3Q2 E) Q1 = 4Q2 /3
11) An electron is released from rest in a uniform electric field. If the electric field is 3.65 kN/C, at the end of 15 ns the electron's velocity will be approximately
A) 9.6 × 106 m/s B) 3.9 × 103 m/s C) 3.1 × 108 m/s D) 5.5 × 103 m/s
E) 7.4 × 106 m/s
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12) A bob of mass m (m = 0.500 g), and charge magnitude Q (Q = 50.0 μC) is held by a massless string in a uniform electric field E. If the bob makes an angle of 10.0 degrees with the vertical, then calculate the magnitude of the electric field E and the sign of the bob charge Q.
A) 1.73 × 101 N/C and Q is positive.B) 9.81 × 101 N/C and Q is negative.C) 9.81 × 101 N/C and Q is positive.D) 1.73 × 101 N/C and Q is negative.E) 1.80 × 10–1 N/C and Q is positive
13) The point P is on the axis of a ring of charge, and all vectors shown lie in the yz plane. The negatively charged ring lies in the xz plane. The vector that correctly represents the direction of the electric field at this point is
A) 1B) 2 C) 3D) 5E) 4
14) An electric dipole consists of a positive charge separated from a negative charge of the same magnitude by a small distance. Which, if any, of the diagrams best represents the electric field lines around an electric dipole?
A) 1B) 2C) 3D) 4E) None of these is correct
15) A uniform line charge of linear charge density λ = 5.00 nC/m extends from x = 0 to x = 10 m. The magnitude of the electric field at the point y = 12 m on the perpendicular bisector of the finite line of charge is
A) 18.8 N/C B) 15.3 N/C C) 9.65 N/C
D) 4.27 N/C E) 2.88 N/C
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16) A conducting circular disk has a uniform positive surface charge density. Which of the following diagrams best represents the electric field lines from the disk? (The disk is drawn as a cross–section.)
A) 1B) 2C) 3D) 4E) none of the diagrams
17) A uniform circular ring has charge Q and radius r. A uniformly charged disk also has charge Q and radius r. Calculate the ratio of the electric field at a distance of r along the axis of the ring to the electric field at a distance of r along the axis of the disk.
A) 1.0 B) 0.60 C) 1.7 D) 0.50 E) 0.85
18) A cube of side 3.56 cm has a charge of 9.11 μC placed at its center. Calculate the electric flux through one side of the cube.
A) 1.03 × 106 N.m2/C B) 2.58 × 105 N.m2/C C) 8.13 × 108 N.m2/C
D) 1.72 × 105 N.m2/C E) 1.35 × 108 N.m2/C
19) A rod of infinite length has a charge per unit length of λ (= q/l). Gauss's law makes it easy to determine that the electric field strength at a perpendicular distance r from the rod is, in terms of k = (4πε0)–1,
A) kλ/r2B) kλ/rC) 4πkλ/rD) 2kλ/rE) zero
20) A sphere of radius 8.0 cm carries a uniform volume charge density ρ = 500 nC/m3.What is the electric field at r = 8.1 cm?
A) 0.12 kN/C B) 1.5 kN/C C) 0.74 kN/C D) 2.3 kN/C E) 12 kN/C
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21) . An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge densityρ = 200 nC/m3. What is the electric field at r = 3.9 cm?
A) zero B) 0.44 kN/C C) 57 N/C D) 0.11 kN/C E) 0.23 kN/C
22) The voltage between the cathode and the screen of a television set is 22 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed just before it hits the screen?
A) 8.8 × 107 m/s B) 2.8 × 106 m/s C) 6.2 × 107 m/s
D) 7.7 × 1015 m/s E) 5.3 × 107 m/s
23) Two equal positive charges are placed x m apart. The equipotential lines are at 100 V intervals
The potential for line c isA) –100 VB) +100 VC) –200 VD) +200 VE) zero
24) The work required to move a third charge, q = –e, from the +100 V line to b is
A) –100 eV B) +100 eV C) –200 eV D) +200 eV E) zero
25) The graph that represents the electric potential near an infinite plane of charge is
A) 1B) 2C) 3D) 4E) 5
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26) A charge of 100 nC resides on the surface of a spherical shell of radius 20 cm. The electric potential at a distance of 50 cm from the center of the spherical shell is
A) 18 VB) 180 VC) 1800 VD) 18,000 VE) None of these is correct
27) Two charged metal spheres are connected by a wire. Sphere A is larger than sphere B, as shown. The magnitude of the electric potential of sphere A
A) is greater than that at the surface of sphere B.B) is less than that at the surface of sphere B.C) is the same as that at the surface of sphere B.D) could be greater than or less than that at the surface of sphere B, depending on theradii of the spheres.E) could be greater than or less than that at the surface of sphere B, depending on thecharges on the spheres
28) A metal ball of charge +Q is lowered into an insulated, uncharged metal shell and allowed to rest on the bottom of the shell. When the charges reach equilibrium
A) the outside of the shell has a charge of –Q and the ball has a charge of +Q.B) the outside of the shell has a charge of +Q and the ball has a charge of +Q.C) the outside of the shell has a charge of zero and the ball has a charge of +Q.D) the outside of the shell has a charge of +Q and the ball has zero charge.E) the ouside of the shell has a charge of +Q and the ball has a charge of –Q.
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Physics
(29)A small, 2.00-g plastic ball is suspended by a 20.0-cmlong string in a uniform electric field, as shown in Figure P23.52. If the ball is in equilibrium when the string makes a 15.0° angle with the vertical, what is the net charge on the ball?
(30) Four identical point charges( q=10 µ)are located on the corners of a rectangle, as shown in Figure P23.55. The dimensions of the rectangle are L = 60cm and W= 17cm. Calculate the magnitude and direction of the net electric force exerted on the charge at the lower left corner by the other three charges.
(31) Two small spheres, each of mass 2.00 g, are suspended by light strings 10.0 cm in length (Fig. P23.62). A uniform electric field is applied in the x direction. The spheres have charges equal to -5.00 * 10-8 C and +5.00 * 10-8 C. Determine the electric field that enables the spheres to be in equilibrium at an angle of ϴ= 10.0.
(32) A solid conducting sphere of radius a carries a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and carries a net charge -Q. Using Gauss’s law, find the electricf ield in the regions labeled ,1 ,2 , and _ in Figure 24.19 nand the charge distribution on the shell when the entire system is in electrostatic equilibrium.
(33) Four closed surfaces, S1 through S4 , together with the charges -2Q, Q, and -Q are sketched in Figure P24.12. Find the electric flux through each surface
(34) A charge of 170 µC is at the center of a cube of side 80.0 cm. (a) Find the total flux through each face of the cube. (b) Find the flux through the whole surface of the cube. (c) Would your answers to parts (a) or (b) change if the charge were not at the center? Explain.
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Physics
(35) A hollow conducting sphere is surrounded by a larger concentric, spherical, conducting shell. The inner sphere has a charge -Q, and the outer sphere has a charge 3Q. The charges are in electrostatic equilibrium. Using Gauss’s law, find the charges and the electric fields everywhere
(36) A solid insulating sphere of radius a carries a net positive charge 3Q, uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b and outer radius c, and having a net charge -Q, as shown in Figure P24.53.
(a) Construct a spherical gaussian surface of radius r >c and find the net charge enclosed by this surface.(b) What is the direction of the electric field at r > c ?(c) Find the electric field at r > c. (d) Find the electric field in the region with radius r where c > r > b.(e) Construct a spherical gaussian surface of radius r , where c > r > b, and find the net charge enclosed bythis surface. (f) Construct a spherical gaussian surface of radius r, where b > r > a, and find the net charge enclosedby this surface. (g) Find the electric field in the region b > r >a.
(37) The charge distribution shown in Figure P25.55 is referred to as a linear quadrupole. (a) Show that the potential at a point on the x axis where x > a is
(b) Show that the expression obtained in part (a) when x>>a reduces to
(38) The x axis is the symmetry axis of a uniformly charged ring of radius R and charge Q (Fig. P25.66). A point Charge Q of mass M is located at the center of the ring. When it is displaced slightly, the point charge accelerates along the x axis to infinity. Show that the ultimate speed of the point charge is
(39) In the circuit illustrated above, switch S is initially open and the battery has been connected for a long time.
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Physics
(a) What is the steady-state current through the ammeter?(b) Calculate the charge on the 10 mF capacitor.(c) Calculate the energy stored in the 5.0 mF capacitor. The switch is now closed, and the circuit comes to a new steady state.(d) Calculate the steady-state current through the battery.(e) Calculate the final charge on the 5.0 mF capacitor.(f) Calculate the energy dissipated as heat in the 40 W resistors in one minute once the circuit has reached steady state
(40) A metal sphere of radius a contains a charge +Q and is surrounded by an uncharged, concentric, metallic shell of inner radius b and outer radius c, as shown above. Express all algebraic answers in terms of the given quantities and fundamental constants.(a) Determine the induced charge on each of the following and explain your reasoning in each case.i. The inner surface of the metallic shellii. The outer surface of the metallic shell(b) Determine expressions for the magnitude of the electric field E as a function of r, the distance from the center of the inner sphere, in each of the following regions.i. r < aii. a < r < biii. b < r < civ. c < r(c) On the axes below, sketch a graph of E as a function of r.
(d) An electron of mass me carrying a charge -e is released from rest at a very large distance from the spheres.Derive an expression for the speed of the particle at a distance 10r from the center of the spheres.
41)
An electric field E exists in the region between the two electrically charged parallel plates shown above.
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Physics
A beam of electrons of mass m, charge q, and velocity v enters the region through a small hole at position A. The electrons exit the region between the plates through a small hole at position B. Express your answers to the following questions in terms of the quantities m, q, E, ϴ, and v. Ignore the effects of gravity.
(a) i. On the diagram of the parallel plates above, draw and label a vector to show the direction ofthe electric field E between the plates.ii. On the following diagram, show the direction of the force(s) acting on an electron after it entersthe region between the plates.iii. On the diagram of the parallel plates above, show the trajectory of an electron that will exit throughthe small hole at position B.(b) Determine the magnitude of the acceleration of an electron after it has entered the region betweenthe parallel plates.(c) Determine the total time that it takes the electrons to go from position A to position B.(d) Determine the distance d between positions A and B.(e) Now assume that the effects of gravity cannot be ignored in this problem. How would the distance d change for an electron entering the region at A and leaving at B? Explain your reasoning.
(42) Two parallel conducting plates, each of area 0.30 m2 , are separated by a distance of 2.0*10 -2 m of air. One plate has charge +Q; the other has charge -Q. An electric field of 5000 N/C is directed to the left in the space between the plates, as shown in the diagram above.
(a) Indicate on the diagram which plate is positive (+) and which is negative (-).(b) Determine the potential difference between the plates.(c) Determine the capacitance of this arrangement of plates.An electron is initially located at a point midway between the plates.(d) Determine the magnitude of the electrostatic force on the electron at this location and state its direction.(e) If the electron is released from rest at this location midway between the plates, determine its speed just before striking one of the plates. Assume that gravitational effects are negligible
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Physics
(43) Two thin metal plates of the same area are given positive charges Q1 and Q2 and kept parallel to each other to form a capacitor of capacitance C. If Q2 > Q1 what will be the potential difference between the plates?
(44) A parallel plate capacitor with air as dielectric has plates of area A and separation d. It is charged to a potential difference V. The charging battery is then disconnected and the plates are pulled apart so that the separation becomes 3d. What is the work done for pulling the plates?
(45) Capacitors C1, C2 and C3 of values 15 μF, 10 μF, 3 μF are connected in series and the series combination is connected across a battery of emf 10 V. When the capacitors are fully charged, the charge on one plate of the 3 μF capacitor will be of magnitude
(a) 10 μC (b) 15 μC (c) 3 μC (d) 20 μC (e) 280 μC
(46) Half of the space between the plates of a parallel plate air capacitor of capacitance C is filled as shown with a material of dielectric constant K. The new capacitance will be(a) KC (b) KC/2(c) (K + 1)C/2(d) 2C/K(e) (K – 1)C
(47) Two concentric thin spherical shells of radii R and r (R > r) share a charge Q so that their surface charge densities are the same. The electric potential at the common centre of the shells is (1/4πε0 = k)
(48) A parallel plate air capacitor with separation d between the plates negligibly small compared to the length and breadth of the plates, is fully charged by connecting it across a battery of emf V volt. If the capacitance of the capacitor is C and the area of each plate is A, the electric field at a point P in between the plates, at distance d/4 from the positive plate (Fig.) is
(49) Two capacitors C1 and C2 are identical in all respects except for the dielectric media between their plates. C1 has air as dielectric where as C2 has a medium of dielectric constant K in place of air. The capacitor C1 is charged to V1 volt and the charging battery is disconnected. Then the uncharged capacitor C2 is connected across C1. If the common voltage across the capacitors is V2, the value of the dielectric constant K is
(50) For transferring a charge +Q coulomb from point A to point B separated by a distance d, the work required to be done by an external agency is –W joule. If the potential of A is V volt, the potential of B will be (in volt)
(a) V + (W/Q) (b) V + (Q/Wd) (c) V + (W/Qd) (d) V – (W/Qd)
(e) V – (W/Q
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