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Copyright 2010 Pearson Education, Inc.Lecture OutlineChapter 20

Physics, 4th EditionJames S. Walker

Chapter 20Electric Potential and Electric Potential Energy

Copyright 2010 Pearson Education, Inc.Units of Chapter 20 Electric Potential Energy and the Electric Potential Energy Conservation The Electric Potential of Point Charges Equipotential Surfaces and the Electric Field Capacitors and Dielectrics Electrical Energy StorageCopyright 2010 Pearson Education, Inc.Work done by electric force is ve if the charge is moved upward. Electric force & displacement are in opposite direction.20-1 Electric Potential Energy and the Electric PotentialThe electric force is conservative; therefore, there must be a potential energy associated with it.

The change in potential energy is the negative of the work:

Copyright 2010 Pearson Education, Inc.20-1 Electric Potential Energy and the Electric Potential

The electron volt is a unit of energy:

(e experiences energy change when passing potential difference of 1V)Copyright 2010 Pearson Education, Inc.20-1 Electric Potential Energy and the Electric PotentialThe electric field is related to how fast the potential is changing:

W=qoEs

Copyright 2010 Pearson Education, Inc.20-1 Electric Potential Energy and the Electric Potential

Copyright 2010 Pearson Education, Inc.20-1 Electric Potential Energy and the Electric Potential

Copyright 2010 Pearson Education, Inc.Question 20.1a Electric Potential Energy I a) protonb) electronc) both feel the same forced) neither there is no forcee) they feel the same magnitude force but opposite direction

electronproton

ElectronProton+-A proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron from the negative side. Which feels the larger electric force?

Copyright 2010 Pearson Education, Inc.9Answer: eQuestion 20.1a Electric Potential Energy I a) protonb) electronc) both feel the same forced) neither there is no forcee) they feel the same magnitude force but opposite direction

electronproton

ElectronProton+-Since F = qE and the proton and electron have the same charge in magnitude, they both experience the same force. However, the forces point in opposite directions because the proton and electron are oppositely charged.A proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron from the negative side. Which feels the larger electric force?Copyright 2010 Pearson Education, Inc.10

electronproton

ElectronProton+-a) protonb) electronc) both feel the same accelerationd) neither there is no acceleratione) they feel the same magnitude acceleration but opposite directionA proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron from the negative side. Which has the larger acceleration?Question 20.1b Electric Potential Energy II

Copyright 2010 Pearson Education, Inc.11Answer: b

electronproton

ElectronProton+-a) protonb) electronc) both feel the same accelerationd) neither there is no acceleratione) they feel the same magnitude acceleration but opposite directionSince F = ma and the electron is much less massive than the proton, the electron experiences the larger acceleration.A proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron from the negative side. Which has the larger acceleration?Question 20.1b Electric Potential Energy II Copyright 2010 Pearson Education, Inc.12

electronproton

ElectronProton+-a) protonb) electronc) both acquire the same KEd) neither there is no change of KEe) they both acquire the same KE but with opposite signsQuestion 20.1c Electric Potential Energy III A proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron from the negative side. When it strikes the opposite plate, which one has more KE?

Copyright 2010 Pearson Education, Inc.13Answer: c

electronproton

ElectronProton+-a) protonb) electronc) both acquire the same KEd) neither there is no change of KEe) they both acquire the same KE but with opposite signsSince PE = qV and the proton and electron have the same charge in magnitude, they both have the same electric potential energy initially. Because energy is conserved, they both must have the same kinetic energy after they reach the opposite plate.Question 20.1c Electric Potential Energy III A proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron from the negative side. When it strikes the opposite plate, which one has more KE?Copyright 2010 Pearson Education, Inc.1420-2 Energy ConservationIn general, for a mass moving from A to B due to a conservative force,

Express e. potential energy in terms of e. potential.

Rearrange,

ABCopyright 2010 Pearson Education, Inc.20-2 Energy ConservationSince the force on a negative charge is opposite to the field direction,Positive charges accelerate in the direction of decreasing electric potential;Negative charges accelerate in the direction of increasing electric potential.

+qCopyright 2010 Pearson Education, Inc.20-3 The Electric Potential of Point ChargesThe difference in potential energy between points A and B is

If at RESTIf RELEASED-qo will accelerates -due to F and +q-K = UV=U/qo andCopyright 2010 Pearson Education, Inc.20-3 The Electric Potential of Point ChargesTherefore, the electric potential of a point charge is:

shown here for a positive and negative charge, respectivelyCopyright 2010 Pearson Education, Inc.20-3 The Electric Potential of Point ChargesSuperposition of electric potential:The algebraic sum of the potentials of each charge.

Copyright 2010 Pearson Education, Inc.20-3 The Electric Potential of Point Charges

Copyright 2010 Pearson Education, Inc.20-3 The Electric Potential of Point Charges

Copyright 2010 Pearson Education, Inc.Which group of charges took more work to bring together from a very large initial distance apart?a+1+1+1dddb+1+2dcBoth took the same amount of work.Question 20.2 Work and Potential Energy

Copyright 2010 Pearson Education, Inc.22Answer: bThe work needed to assemble a collection of charges is the same as the total PE of those charges:

Which group of charges took more work to bring together from a very large initial distance apart?a+1+1+1dddb+1+2dcBoth took the same amount of work.For case 1: only 1 pair

For case 2: there are 3 pairs

added over all pairsQuestion 20.2 Work and Potential EnergyCopyright 2010 Pearson Education, Inc.23a) V > 0b) V = 0c) V < 0

ABWhat is the electric potential at point A?Question 20.3a Electric Potential I

Copyright 2010 Pearson Education, Inc.24Answer: aSince Q2 (which is positive) is closer to point A than Q1 (which is negative) and since the total potential is equal to V1 + V2, the total potential is positive.a) V > 0b) V = 0c) V < 0

ABWhat is the electric potential at point A?Question 20.3a Electric Potential ICopyright 2010 Pearson Education, Inc.25a) V > 0b) V = 0c) V < 0

ABWhat is the electric potential at point B?Question 20.3b Electric Potential II

Copyright 2010 Pearson Education, Inc.26Answer: bSince Q2 and Q1 are equidistant from point B, and since they have equal and opposite charges, the total potential is zero.a) V > 0b) V = 0c) V < 0

ABWhat is the electric potential at point B?Question 20.3b Electric Potential IIFollow-up: What is the potential at the origin of the x y axes?Copyright 2010 Pearson Education, Inc.2720-4 Equipotential Surfaces and the Electric FieldOn a contour map, the curves mark constant elevation (height);The closer together the curves, the steeper the slope.

Copyright 2010 Pearson Education, Inc.20-4 Equipotential Surfaces and the Electric FieldElectric potential and the electric field have the same relationship there are lines (or, in three dimensions, surfaces) of constant potential. The electric field is perpendicular to these equipotential lines, and strongest where the lines are closest together.

Copyright 2010 Pearson Education, Inc.20-4 Equipotential Surfaces and the Electric Field

(a)(b)E FieldIn between is very weak (cancel each other)Very strong in betweenE potentialConstant between the charges.Changes rapidlyCopyright 2010 Pearson Education, Inc.20-4 Equipotential Surfaces and the Electric FieldAn ideal conductor is an equipotential surface. Therefore, if two conductors are at the same potential, the one that is more curved will have a larger electric field around it. This is also true for different parts of the same conductor.

Copyright 2010 Pearson Education, Inc.Four point charges are arranged at the corners of a square. Find the electric field E and the potential V at the center of the square.a) E = 0 V = 0b) E = 0 V 0c) E 0 V 0d) E 0 V = 0e) E = V regardless of the value-Q-Q+Q+QQuestion 20.4 Hollywood Square

Copyright 2010 Pearson Education, Inc.32Answer: dFour point charges are arranged at the corners of a square. Find the electric field E and the potential V at the center of the square.a) E = 0 V = 0b) E = 0 V 0c) E 0 V 0d) E 0 V = 0e) E = V regardless of the value-Q-Q+Q+Q The potential is zero: the scalar contributions from the two positive charges cancel the two minus charges. However, the contributions from the electric field add up as vectors, and they do not cancel (so it is non-zero).Question 20.4 Hollywood SquareFollow-up: What is the direction of the electric field at the center?Copyright 2010 Pearson Education, Inc.33Which of these configurations gives V = 0 at all points on the x axis?d) all of the above e) none of the abovea)x+2mC-2mC+1mC-1mCb)x+2mC-1mC+1mC-2mCc)x+2mC-1mC-2mC+1mCQuestion 20.5b Equipotential Surfaces II

Copyright 2010 Pearson Education, Inc.34Answer: aOnly in case (1), where opposite charges lie directly across the x axis from each other, do the potentials from the two charges above the x axis cancel the ones below the x axis.Which of these configurations gives V = 0 at all points on the x axis?d) all of the above e) none of the abovea)x+2mC-2mC+1mC-1mCb)x+2mC-1mC+1mC-2mCc)x+2mC-1mC-2mC+1mCQuestion 20.5b Equipotential Surfaces IICopyright 2010 Pearson Education, Inc.35Which of these configurations gives V = 0 at all points on the y axis?d) all of the above e) none of the aboveQuestion 20.5c Equipotential Surfaces IIIa)x+2mC-2mC+1mC-1mCb)x+2mC-1mC+1mC-2mCc)x+2mC-1mC-2mC+1mC

Copyright 2010 Pearson Education, Inc.36Answer: cWhich of these configurations gives V = 0 at all points on the y axis?d) all of the above e) none of the aboveQuestion 20.5c Equipotential Surfaces IIIa)x+2mC-2mC+1mC-1mCb)x+2mC-1mC+1mC-2mCc)x+2mC-1mC-2mC+1mCOnly in case (3), where opposite charges lie directly across the y axis from each other, do the potentials from the two charges above the y axis cancel the ones below the y axis.Copyright 2010 Pearson Education, Inc.37Which two points have the same potential?a) A and Cb) B and Ec) B and Dd) C and Ee) no pairACBDEQQuestion 20.6 Equipotential of Point Charge

Copyright 2010 Pearson Education, Inc.38Answer: d Since the potential of a point charge is:

only points that are at the same distance from charge Q are at the same potential. This is true for points C and E. They lie on an equipotential surface.Which two points have the same potential?a) A and Cb) B and Ec) B and Dd) C and Ee) no pairACBDEQ

Question 20.6 Equipotential of Point ChargeFollow-up: Which point has the smallest potential?Copyright 2010 Pearson Education, Inc.39

20-5 Capacitors and DielectricsA capacitor is two conducting plates separated by a finite distance:Copyright 2010 Pearson Education, Inc.

The capacitance relates the charge to the potential difference:20-5 Capacitors and Dielectrics

Michael Faraday:Pioneer researcher in electricity & magnetismCopyright 2010 Pearson Education, Inc.20-5 Capacitors and DielectricsA simple type of capacitor is the parallel-plate capacitor. It consists of two plates of area A separated by a distance d.

By calculating the electric field created by the charges Q, we find that the capacitance of a parallel-plate capacitor is:

Copyright 2010 Pearson Education, Inc.20-5 Capacitors and DielectricsThe general properties of a parallel-plate capacitor is that the capacitance increases as the plates become larger and decreases as the separation increases.Copyright 2010 Pearson Education, Inc.20-5 Capacitors and Dielectrics

Copyright 2010 Pearson Education, Inc.20-5 Capacitors and Dielectrics

Copyright 2010 Pearson Education, Inc.

20-5 Capacitors and DielectricsA dielectric is an insulator; when placed between the plates of a capacitor it gives a lower potential difference with the same charge, due to the polarization of the material. This increases the capacitance.Copyright 2010 Pearson Education, Inc.20-5 Capacitors and DielectricsThe polarization of the dielectric results in a lower electric field within it; the new field, E is given by dividing the original field, Eo by the dielectric constant :

Therefore, the new capacitance, C becomes:

Copyright 2010 Pearson Education, Inc.20-5 Capacitors and DielectricsThe dielectric constant is a property of the material; here are some examples:

Copyright 2010 Pearson Education, Inc.20-5 Capacitors and Dielectrics

Copyright 2010 Pearson Education, Inc.20-5 Capacitors and Dielectrics

Copyright 2010 Pearson Education, Inc.Capacitor C1 is connected across a battery of 5 V. An identical capacitor C2 is connected across a battery of 10 V. Which one has more charge?a) C1b) C2c) both have the same charged) it depends on other factorsQuestion 20.8 Capacitors

Copyright 2010 Pearson Education, Inc.51Answer: bSince Q = CV and the two capacitors are identical, the one that is connected to the greater voltage has more charge, which is C2 in this case.Capacitor C1 is connected across a battery of 5 V. An identical capacitor C2 is connected across a battery of 10 V. Which one has more charge?a) C1b) C2c) both have the same charged) it depends on other factorsQuestion 20.8 CapacitorsCopyright 2010 Pearson Education, Inc.52a) increase the area of the plates b) decrease separation between the platesc) decrease the area of the platesd) either a) or b)e) either b) or c)What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)?

+QQQuestion 20.9a Varying Capacitance I

Copyright 2010 Pearson Education, Inc.53Answer: d Since Q = CV, in order to increase the charge that a capacitor can hold at constant voltage, one has to increase its capacitance. Since the capacitance is given by , that can be done by either increasing A or decreasing d. a) increase the area of the plates b) decrease separation between the platesc) decrease the area of the platesd) either a) or b)e) either b) or c)

What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)?

+QQQuestion 20.9a Varying Capacitance ICopyright 2010 Pearson Education, Inc.54A parallel-plate capacitor initially has a potential difference of 400 V and is then disconnected from the charging battery. If the plate spacing is now doubled (without changing Q), what is the new value of the voltage?a) 100 V b) 200 Vc) 400 Vd) 800 Ve) 1600 V

+QQQuestion 20.9c Varying Capacitance III

Copyright 2010 Pearson Education, Inc.55Answer: dOnce the battery is disconnected, Q has to remain constant, since no charge can flow either to or from the battery. Since , when the spacing d is doubled, the capacitance C is halved. And since Q = CV, that means the voltage must double.A parallel-plate capacitor initially has a potential difference of 400 V and is then disconnected from the charging battery. If the plate spacing is now doubled (without changing Q), what is the new value of the voltage?a) 100 V b) 200 Vc) 400 Vd) 800 Ve) 1600 V

+QQ

Question 20.9c Varying Capacitance IIICopyright 2010 Pearson Education, Inc.5620-6 Electrical Energy StorageBy considering how much energy it takes to move an increment of charge, Q, from one plate to the other across the potential difference, V we can find the total energy stored in the capacitor:

Copyright 2010 Pearson Education, Inc.Summary of Chapter 20 Electric force is conservative, and has a potential energy associated with it Change in electric potential energy: Change in electric potential: Relation between electric field and electric potential:

Total energy (electric potential energy plus kinetic energy) is conserved

Copyright 2010 Pearson Education, Inc.Summary of Chapter 20 Positive charges accelerate in the direction of increasing potential Negative charges accelerate in the direction of decreasing potential Electric potential of a point charge: Electric potential energy of two point charges:

Total electric potential and total electric potential energy are sums of those due to individual charges

Copyright 2010 Pearson Education, Inc.Summary of Chapter 20 Equipotential surfaces are those on which the electric potential is constant. The electric field is perpendicular to the equipotential surfaces. Ideal conductors are equipotential surfaces. A capacitor is a device that stores electric charge. Capacitance:

Copyright 2010 Pearson Education, Inc.Summary of Chapter 20 Capacitance of a parallel-plate capacitor:

A dielectric is an insulator that increases a capacitors capacitance. A dielectric is characterized by its dielectric constant. A sufficiently large electric field can cause a dielectric to break down.

Copyright 2010 Pearson Education, Inc.Summary of Chapter 20 A capacitor also stores electric energy. Electric energy stored in a capacitor:

Energy density in an electric field:

Copyright 2010 Pearson Education, Inc.