Chapter 16

MS101: Physics

Chapter 16: Electric Forces and FieldsDr. Ahmed Amin Hussein01007903935

ahussein32125@gmail.com2013-201422 December 2013Prepared By: Dr. Ahmed Amin1Chapter 16: Electric Forces and FieldsElectric ChargeConductors & InsulatorsCoulombs LawElectric FieldMotion of a Point Charge in a Uniform E-fieldConductors in Electrostatic EquilibriumGausss Law22 December 2013Prepared By: Dr. Ahmed Amin216.1 Electric ChargeThere are two kinds of electric charge: positive and negative.A body is electrically neutral if the sum of all the charges in a body is zero.Charge is a conserved quantity.22 December 2013Prepared By: Dr. Ahmed Amin33Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Questions 1, 2, and 3. Electrical ChargeAn object with an excess of electrons is negatively charged.An object with too few electrons (too many protons) is positively charged.An object with the same number of electrons and protons is neutral.Charge is ConservedElectric charge is conserved -Electric charge moves from one place to another - no case of the net creation or destruction of electric charge has ever been observed.In solids, only electrons can move.In liquids, gasses, and plasmas, both positive and negative ions are free to move.Electric ChargeObjects can lose or gain electric charges.

The net charge is also sometimes called excess charge because a charged object has an excess of either positive or negative charges.

A tiny imbalance in either positive or negative charge on an object is the cause of static electricity.

22 December 2013Prepared By: Dr. Ahmed Amin6Units of ChargeThe SI unit of charge is the Coulomb.

1 Coulomb = the charge of 6.24 x 1018 electronsConservation of ChargeCharged particles can be transferred from one object to another, but the total amount of charge is conserved. Example: An object with 5 excess units of positive charge and another with 2 units of excess negative charge are released from rest and attract each other. (By Newtons 3rd law, the forces are equal strength, opposite directions, but their accelerations depend on their masses too.) Since there is no net force on the system, their center of mass does not accelerate, and they collide there. As they fall toward each other, electric potential energy is converted to kinetic energy. When contact is made charge may be exchanged but they total amount before and after must be the same. After the collision the total momentum must still be zero.+5-2BeforeTotal charge: +3+1.5+1.5 AfterTotal charge: +322 December 2013Prepared By: Dr. Ahmed Amin88The elementary unit of charge is e = 1.60210-19 C.The charge on the electron is 1e.The charge on the proton is +1e.The charge on the neutron is 0e.Experiments show that likes charges will repel each other and unlike charges will attract each other and that the force decreases with increasing distance between charges.22 December 2013Prepared By: Dr. Ahmed Amin9The charge of an object, Q, is always a multiple of this elementary charge: Q = N e, where N is an integer. Electric ChargeAll ordinary matter contains both positive and negative charge.

You do not usually notice the charge because most matter contains the exact same number of positive and negative charges.

An object is electrically neutral when it has equal amounts of both types of charge.

22 December 2013Prepared By: Dr. Ahmed Amin10An object can become polarized if the charges within it can be separated. +++++This body is electrically neutral.By holding a charged rod near the body, it can be polarized.++++++++++22 December 2013Prepared By: Dr. Ahmed Amin11PolarizationBringing a charged object near (but not touching) a neutral object polarizes (temporarily separates) the charge of the neutral object.Like charges in the neutral object are repelled by the charged object.Unlike charges in the neutral object are attracted by the neutral object.The neutral object returns to normal when the charged object is removed.Electric DipolesAn object that is electrically neutral overall, but permanently polarized, is called an electric dipole.Example: H20 moleculeExample (text problem 16.4): A metallic sphere has a charge of +4.0 nC. A negatively charged rod has a charge of 6.0 nC. When the rod touches the sphere, 8.2109 electrons are transferred. What are the charges of the sphere and the rod now?Each electron has a charge 1.60210-19 C so the total charge transferred is (8.2109 1.60210-19 ) 1.3 nC.The rod is left with 6.0 nC + 1.3 nC = 4.7 nC of charge and the sphere now has +4.0 nC 1.3 nC = +2.7 nC of charge.22 December 2013Prepared By: Dr. Ahmed Amin1416.2 Conductors and InsulatorsA conductor is made of material that allows electric charge to move through it easily.An insulator is made of material that does not allow electric charge to move through it easily.22 December 2013Prepared By: Dr. Ahmed Amin1515Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 4. Insulators vs. Conductors A conductor is a material in which excess charge freely flows. Metals are typically excellent conductors because the valence (outer shell) electrons in metal atoms are not confined to any one atom. Rather, they roam freely about a metal object. Metal are excellent conductors of electricity (and heat) for this reason.An insulator is a material in which excess charge, for the most part, resides where it is deposited. That is, once placed, it does not move. Most nonmetallic material are good insulators. Valence electrons are much more tightly bound to the atoms and are not free to roam about. Insulators are useful for studying electrostatics (the study of charge that can be localized and contained).Semi-conductors, like silicon used in computer chips, have electrical conductivity between that of conductors and insulators. 22 December 2013Prepared By: Dr. Ahmed Amin1616Conductors & InsulatorsMaterials in which charges are free to move about are called conductors.Materials in which charges are not free to move about are called insulators.

SemiconductorsSemiconductors are materials which are good insulators in pure form, but their conducting properties can be adjusted over a wide range by introducing very small amounts of impurities.Silicon, germanium, etc.Transistors, computer chips, etc.SuperconductorsSuperconductors are materials that lose all resistance to charge movement at temperatures near absolute zero (0 K or about -273oC).Recently, high temperature (above 100 K) superconductors have been discovered.16.3 Coulombs Law

The magnitude of the force between two point charges is:where q1 and q2 are the charges, r is the separation between the two charges and k = 8.99109 Nm2/C2.

and 0 is called the permittivity of free space.22 December 2013Prepared By: Dr. Ahmed Amin2020Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Questions 5, 6, 7, 8, and 9. rq1q2F21F12rq1q2F21F12The electric force is directed between the centers of the two point charges.The electric force is an example of a long-range or field force, just like the force of gravity.Attractive force between q1 and q2.Repulsive force between q1 and q2.22 December 2013Prepared By: Dr. Ahmed Amin21Example: What is the net force on the charge q1 due to the other two charges? q1 = +1.2 C, q2 = 0.60 C, and q3 = +0.20 C.The net force on q1 is Fnet = F21 + F31

F31F2122 December 2013Prepared By: Dr. Ahmed Amin22The magnitudes of the forces are: Example continued:

22 December 2013Prepared By: Dr. Ahmed Amin23Example continued:The components of the net force are:

Where from the figure

22 December 2013Prepared By: Dr. Ahmed Amin24Example continued:The magnitude of the net force is:

The direction of the net force is:22 December 2013Prepared By: Dr. Ahmed Amin25Example (text problem 16.11): What is the ratio of the electric force and gravitational force between a proton and an electron separated by 5.310-11 m (the radius of a Hydrogen atom)?

The ratio is:

22 December 2013Prepared By: Dr. Ahmed Amin26MCQ- 1-BHow many electrons does it take to make one coulomb of negative charge?A.1.00 109B.6.25 1018C.6.02 1023D.1.66 1018E.2.24 10422 December 2013Prepared By: Dr. Ahmed Amin27MCQ- 2-DArrange the following from smallest to largest.

A.mC, C, nC, pCB.C, mC, pC, nCC.nC, pC, mC, CD.pC, nC, C, mCE.nC, pC, C, mC22 December 2013Prepared By: Dr. Ahmed Amin28

MCQ- 1-CThree point charges are positioned as follows: q1 is at (0.00 m, 0.00 m), q2 is at (1.20 m, 0.00 m), and q3 is at (1.20 m, 1.60 m). If all three charges are negative, into which quadrant is the force on q1 pointing?A.1stB.2ndC.3rdD.4thE.there isn't enough information in the problem to solve this22 December 2013Prepared By: Dr. Ahmed Amin29HW - 1+0.80 C-0.60 C+1.0 C10.0 cm8.0 cmThree point charges are fixed in place in a right triangle. What is the electric force on the -0.60 C charge due to the other two charges?22 December 2013Prepared By: Dr. Ahmed Amin30HW - 2+0.80 C-0.60 C+1.0 C10.0 cm8.0 cmThree point charges are fixed in place in a right triangle. What is the electric force on the +1.0 C charge due to the other two charges?22 December 2013Prepared By: Dr. Ahmed Amin31HW - 3A total charge of 7.50 X 10-6 C is distributed on two different small metal spheres. When the spheres are 6.00 cm apart, they each feel a repulsive force of 20.0 N. How much charge is on each sphere. (6.21 C and 1.29 C)22 December 2013Prepared By: Dr. Ahmed Amin32Electric Force Example++15 mA proton and an electron are separated by 15 m. They are released from rest. Our goal is to find the acceleration each undergoes at the instant of release. Find the electric force on each particle.

Find the gravitational force on each particle. A protons mass is 1.67 10-27 kg, and an electrons mass is 9.11 10-31 kg.

Find the net force on each and round appropriately. Note that the gravitational force is inconsequential here.

Find the acceleration on each particle.

Why couldnt we use kinematics to find the time it would take the particles to collide?1.024 10-18 N4.51 10-58 N1.024 10-18 Ne-: 1.124 1012 m/s2, p+: 6.13 108 m/s2r changes, so F changes, so a changes.22 December 2013Prepared By: Dr. Ahmed Amin3333System of 3 Charges17 cm14 cm 115+3 C-5 C+2 CAC BIn a system of three point charges, each charge exerts a forces on the other two. So, here weve got a vector net force problem. Find the net force on charge B. Steps:Find the distance in meters between A and B using the law of cosines.Find angle B in the triangle using the law of sines.

Find FBA (the magnitude of the force on charge B due to charge A).Find FBC.Break up the forces on B into components and find the net horiz. & vertical forces.

Determine Fnet on B.0.261947 m36.027932 0.786981 N4.591836 N3.78 N (right) , 1.25 N (up) 3.98 N at18.3 N of E22 December 2013Prepared By: Dr. Ahmed Amin3434System of 4 Charges-16 C+9 C-7 C+25 C3 cm4 cmABCDHere four fixed charges are arranged in a rectangle. Find Fnet on charge D.

Solution:767.2 N at 59.6 N of W22 December 2013Prepared By: Dr. Ahmed Amin3535Hanging Charge Problemq, mq, mLLmg TFETwo objects of equal charge and mass are hung from the same point on a ceiling with equally long strings. They repel each other forming an angle between the strings. Find q as a function of m, L and .

Solution: Draw a FBD on one of the objects, break T into components, and write net vertical and horizontal equations:T sin( / 2) = FE , T cos( / 2) = mg. Dividing equations and using Coulombs law yields:mg tan( / 2) = FE = Kq 2 / r 2, where r = 2 L sin( / 2). Thus, q = 4 L2 mg tan( / 2) sin2( / 2)K 22 December 2013Prepared By: Dr. Ahmed Amin3636Thank YouQUESTIONS ?22 December 2013Prepared By: Dr. Ahmed Amin37The End383916.4 The Electric Field

Recall :

Where g is the strength of the gravitational field.Similarly for electric forces we can define the strength of the electric field E.39Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Questions 10, 11, 12, 13, 16, and 18. 40

For a point charge of charge Q, the magnitude of the force per unit charge at a distance r (the electric field) is: The electric field at a point in space is found by adding all of the electric fields present.

Be careful! The electric field is a vector!41Example: Find the electric field at the point P.E is a vector. What is its direction?Place a positive test charge at the point of interest. The direction of the electric field at the location of the test charge is the same as the direction of the force on the test charge.q1 = +ex = 0 mq2 = 2ex = 1 mPx = 2 mx42Locate the positive test charge here.Direction of E due to charge 2Direction of E due to charge 1q1 = +eq2 = 2ePxExample continued:Pq1 = +eq2 = 2ex43The net electric field at point P is:

The magnitude of the electric field is:

Example continued:44Example continued:

The net E-field is directed to the left.45Electric field linesElectric field lines are a useful way to indicate what the magnitude and direction of an electric field is in space.Rules:The direction of the E-field is tangent to the field lines at every point in space.The field is strong where there are many field lines and weak where there are few lines.The field lines start on + charges and end on charges.Field lines do not cross.46Pictorial representation of the rules on the previous slide:

4716.5 Motion of a Point Charge in a Uniform E-Field A region of space with a uniform electric field containing a particle of charge q (q > 0) and mass m. 47Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 14.48FBD for the charge q

Apply Newtons 2nd Law and solve for the acceleration.FexyOne could now use the kinematic equations to solve for distance traveled in a time interval, the velocity at the end of a time interval, etc.49Example: What electric field strength is needed to keep an electron suspended in the air?FBD for the electron:xyFewTo get an upward force on the electron, the electric field must be directed toward the Earth.50Apply Newtons 2nd Law:

Example continued:51Example (text problem 16.50): A horizontal beam of electrons moving 4.0107 m/s is deflected vertically by the vertical electric field between two oppositely charged parallel plates. The magnitude of the field is 2.00104 N/C. (a) What is the direction of the field between the plates?

From the top plate to the bottom plate52(b) What is the charge per unit area on the plates?

This is the electric field between two charged plates.

Note that E here is independent of the distance from the plates!Example continued:53FBD for an electron in the beam:(c) What is the vertical deflection d of the electrons as they leave the plates?

Apply Newtons 2nd Law and solve for the acceleration:xyFewExample continued:54What is the vertical position of the electron after it travels a horizontal distance of 2.0 cm?

0

0

Time interval to travel 2.00 cm horizontallyDeflection of an electron in the beamExample continued:5516.6 Conductors in Electrostatic EquilibriumConductors are easily polarized. These materials have free electrons that are free to move around inside the material. Any charges that are placed on a conductor will arrange themselves in a stable distribution. This stable situation is called electrostatic equilibrium.55Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 15.56When a conductor is in electrostatic equilibrium, the E-field inside it is zero.Any net charge must reside on the surface of a conductor in electrostatic equilibrium.57Just outside the surface of a conductor in electrostatic equilibrium the electric field must be perpendicular to the surface. If this were not true, then any surface charge would have a net force acting on it, and the conductor would not be in electrostatic equilibrium.58Any excess charge on the surface of a conductor will accumulate where the surface is highly curved (i.e. a sharp point).

5916.7 Gausss Law+QEnclose a point charge +Q with an imaginary sphere.Here, E-field lines exit the sphere.59Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Questions 17, 19, and 20. 60Look at a small patch of the surface of the imaginary sphere.With a positive charge inside the sphere you would see electric field lines leaving the surface.61Recall that

It is only the component of the electric field that is perpendicular to the surface that exits the surface.

so that theESurfaceEperpEpar62Define a quantity called flux, which is related to the number of field lines that cross a surface:

This angle is measured from the normal to the surface.Flux > 0 when field lines exit the surface and flux < 0 when field lines enter the surface.Enormal63Example (text problem 16.62): Find the electric flux through each side of a cube of edge length a in a uniform electric field of magnitude E.A cube has six sides: The field lines enter one face and exit through another. What is the flux through each of the other four faces?64The flux through the left face is EA.The flux through the right face is +EA. The net flux through the cube is zero.There is zero electric flux though the other four faces. The electric field lines never enter/exit any of them. Example continued:65This is Gausss Law.

The flux through a surface depends on the amount of charge inside the surface. Based on this, the cube in the previous example contained no net charge.Since Eq, the flux through a surface can also be written as 66SummaryProperties of Conductors/InsulatorsCharge PolarizationCoulombs LawThe Electric FieldMotion of a Point Charge in an Electric FieldGausss Law