1. ConcepTest 16.1aElectric Potential Energy I ConcepTest 16.1a Electric Potential Energy Ielectron proton electron proton + - 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? 1) proton 2) electron 3) both feel the same force 4) neither–there is no force 5) they feel the same magnitude force but in opposite directions

2. ConcepTest 16.1aElectric Potential Energy I ConcepTest 16.1a Electric Potential Energy I 1) proton 2) electron 3) both feel the same force 4) neither–there is no force 5) they feel the same magnitude force but in opposite directions electron proton electron proton + - F = qE same charge in magnitude same force opposite directions oppositely charged 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?

3. electron proton electron proton + - 1) proton 2) electron 3) both feel the same acceleration 4) neither–there is no acceleration 5) they feel the same magnitude acceleration but in opposite directions 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? ConcepTest 16.1bElectric Potential Energy II ConcepTest 16.1b Electric Potential Energy II

4. electron proton electron proton + - F = maelectron is much less massiveelectron experiences the larger acceleration Since F = ma and the electron is much less massive than the proton, then 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? ConcepTest 16.1bElectric Potential Energy II ConcepTest 16.1b Electric Potential Energy II 1) proton 2) electron 3) both feel the same acceleration 4) neither–there is no acceleration 5) they feel the same magnitude acceleration but in opposite directions

5. electron proton electron proton + - 1) proton 2) electron 3) both acquire the same KE 4) neither – there is no change of KE 5) they both acquire the same KE but with opposite signs ConcepTest 16.1cElectric Potential Energy III ConcepTest 16.1c 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?

6. electron proton electron proton + - PE = qV same charge in magnitude same electric potential energy same kinetic energy Since 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. ConcepTest 16.1cElectric Potential Energy III ConcepTest 16.1c 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? 1) proton 2) electron 3) both acquire the same KE 4) neither – there is no change of KE 5) they both acquire the same KE but with opposite signs

7. Which group of charges took more work to bring together from a very large initial distance apart? +1 dd d +2 d Both took the same amount of work ConcepTest 16.2Work and Potential Energy ConcepTest 16.2 Work and Potential Energy

8. total PE The 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? +1 dd d +2 d Both took the same amount of work For case 1: only 1 pair For case 2: there are 3 pairs added over all pairs ConcepTest 16.2Work and Potential Energy ConcepTest 16.2 Work and Potential Energy

9. 1) V > 0 2) V = 0 3) V < 0 A B What is the electric potential at point A? ConcepTest 16.3aElectric Potential I ConcepTest 16.3a Electric Potential I

10. positivecloser positive Since Q 2 (which is positive) is closer to point A than Q 1 (which is negative), and since the total potential is equal to V 1 + V 2, then the total potential is positive. 1) V > 0 2) V = 0 3) V < 0 A B What is the electric potential at point A? ConcepTest 16.3aElectric Potential I ConcepTest 16.3a Electric Potential I

11. 1) V > 0 2) V = 0 3) V < 0 A B What is the electric potential at point B? ConcepTest 16.3bElectric Potential II ConcepTest 16.3b Electric Potential II

12. zero Since Q 2 and Q 1 are equidistant from point B, and since they have equal and opposite charges, then the total potential is zero. 1) V > 0 2) V = 0 3) V < 0 A B What is the electric potential at point B? ConcepTest 16.3bElectric Potential II ConcepTest 16.3b Electric Potential II Follow-up: What is the potential at the origin of the x-y axes?

13. 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. 1) E = 0 V = 0 2) E = 0 V  0 3) E  0 V  0 4) E  0 V = 0 5) E = V regardless of the value -Q-Q-Q-Q -Q-Q-Q-Q +Q+Q+Q+Q +Q+Q+Q+Q ConcepTest 16.4Hollywood Square ConcepTest 16.4 Hollywood Square

14. 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. 1) E = 0 V = 0 2) E = 0 V  0 3) E  0 V  0 4) E  0 V = 0 5) E = V regardless of the value -Q-Q-Q-Q -Q-Q-Q-Q +Q+Q+Q+Q +Q+Q+Q+Q potential is zero The potential is zero: the scalar contributions from the two positive charges cancel the two minus charges. it is non-zero However, the contributions from the electric field add up as vectors, and they do not cancel (so it is non-zero). ConcepTest 16.4Hollywood Square ConcepTest 16.4 Hollywood Square Follow-up: What is the direction of the electric field at the center?

15. At which point does V = 0? 1 3 2 4 +Q+Q–Q–Q 5) all of them ConcepTest 16.5aEquipotential Surfaces I ConcepTest 16.5a Equipotential Surfaces I

16. At which point does V = 0? 1 3 2 4 +Q+Q–Q–Q 5) all of them All of the points are equidistant from both charges cancel outeverywhere All of the points are equidistant from both charges. Since the charges are equal and opposite, their contributions to the potential cancel out everywhere along the mid-plane between the charges. ConcepTest 16.5aEquipotential Surfaces I ConcepTest 16.5a Equipotential Surfaces I Follow-up: What is the direction of the electric field at all 4 points?

17. Which two points have the same potential? 1) A and C 2) B and E 3) B and D 4) C and E 5) no pair A C B D E Q ConcepTest 16.6Equipotential of Point Charge ConcepTest 16.6 Equipotential of Point Charge

18. Since the potential of a point charge is: same distance same potential only points that are at the same distance from charge Q are at the same potential. This is true for points C and E. Equipotential Surface They lie on an Equipotential Surface. Which two points have the same potential? 1) A and C 2) B and E 3) B and D 4) C and E 5) no pair A C B D E Q ConcepTest 16.6Equipotential of Point Charge ConcepTest 16.6 Equipotential of Point Charge Follow-up: Which point has the smallest potential?

19. Which requires the most work, to move a positive charge from P to point 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 16.7aWork and Electric Potential I ConcepTest 16.7a Work and Electric Potential I

20. path 1 against hard to do For path 1, you have to push the positive charge against the E field, which is hard to do. By contrast, path #4 is the easiest, since the field does all the work. Which requires the most work, to move a positive charge from P to point 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 16.7aWork and Electric Potential I ConcepTest 16.7a Work and Electric Potential I

21. Which requires zero work, to move a positive charge from P to point 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 16.7bWork and Electric Potential II ConcepTest 16.7b Work and Electric Potential II

22. path 3 For path 3, you are moving in a direction perpendicular to the field lines. This means you are moving along an equipotential, which requires no work (by definition). Which requires zero work, to move a positive charge from P to point 1, 2, 3 or 4 ? All points are the same distance from P. 1) P  1 2) P  2 3) P  3 4) P  4 5) all require the same amount of work P 1 2 3 4 ConcepTest 16.7bWork and Electric Potential II ConcepTest 16.7b Work and Electric Potential II Follow-up: Which path requires the least work?

23. Capacitor C 1 is connected across a battery of 5 V. An identical capacitor C 2 is connected across a battery of 10 V. Which one has the most charge? C 1 1) C 1 C 2 2) C 2 3) both have the same charge 4) it depends on other factors ConcepTest 16.8Capacitors ConcepTest 16.8 Capacitors

24. Q = C V greater voltagemost charge C 2 Since Q = C V and the two capacitors are identical, the one that is connected to the greater voltage has the most charge, which is C 2 in this case. Capacitor C 1 is connected across a battery of 5 V. An identical capacitor C 2 is connected across a battery of 10 V. Which one has the most charge? C 1 1) C 1 C 2 2) C 2 3) both have the same charge 4) it depends on other factors ConcepTest 16.8Capacitors ConcepTest 16.8 Capacitors

25. increase the area of the plates 1) increase the area of the plates decrease separation between the plates 2) decrease separation between the plates 3) decrease the area of the plates 4) either (1) or (2) 5) either (2) or (3) What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)? +Q –Q ConcepTest 16.9aVarying Capacitance I ConcepTest 16.9a Varying Capacitance I

26. Q = C V increase its capacitance increasing Adecreasing d Since Q = C V, 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. increase the area of the plates 1) increase the area of the plates decrease separation between the plates 2) decrease separation between the plates 3) decrease the area of the plates 4) either (1) or (2) 5) either (2) or (3) What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)? +Q –Q ConcepTest 16.9aVarying Capacitance I ConcepTest 16.9a Varying Capacitance I

27. +Q+Q –Q–Q A parallel-plate capacitor initially has a voltage of 400 V and stays connected to the battery. If the plate spacing is now doubled, what happens? the voltage decreases 1) the voltage decreases the voltage increases 2) the voltage increases the charge decreases 3) the charge decreases the charge increases 4) the charge increases both voltage and charge change 5) both voltage and charge change ConcepTest 16.9bVarying Capacitance II ConcepTest 16.9b Varying Capacitance II

28. Since the battery stays connected, the voltage must remain constant ! Q = C Vcharge must decrease Since the battery stays connected, the voltage must remain constant ! Since, when the spacing d is doubled the capacitance C is halved. And since Q = C V, that means the charge must decrease. +Q+Q –Q–Q A parallel-plate capacitor initially has a voltage of 400 V and stays connected to the battery. If the plate spacing is now doubled, what happens? the voltage decreases 1) the voltage decreases the voltage increases 2) the voltage increases the charge decreases 3) the charge decreases the charge increases 4) the charge increases both voltage and charge change 5) both voltage and charge change ConcepTest 16.9bVarying Capacitance II ConcepTest 16.9b Varying Capacitance II Follow-up: How do you increase the charge?

29. 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? 100 V 1) 100 V 200 V 2) 200 V 3) 400 V 4) 800 V 5) 1600 V +Q+Q –Q–Q ConcepTest 16.9cVarying Capacitance III ConcepTest 16.9c Varying Capacitance III

30. Once the battery is disconnected, Q has to remain constant Q = C V voltage must double Once 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 = C V, 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? 100 V 1) 100 V 200 V 2) 200 V 3) 400 V 4) 800 V 5) 1600 V +Q+Q –Q–Q ConcepTest 16.9cVarying Capacitance III ConcepTest 16.9c Varying Capacitance III

31. ConcepTest 16.10aCapacitors I ConcepTest 16.10a Capacitors I o o C C C C eq 1) C eq = 3/2 C 2) C eq = 2/3 C 3) C eq = 3 C 4) C eq = 1/3 C 5) C eq = 1/2 C What is the equivalent capacitance,, of the combination below? What is the equivalent capacitance, C eq, of the combination below?

32. series inverses1/2 C parallel directly 3/2 C The 2 equal capacitors in series add up as inverses, giving 1/2 C. These are parallel to the first one, which add up directly. Thus, the total equivalent capacitance is 3/2 C. ConcepTest 16.10aCapacitors I ConcepTest 16.10a Capacitors I o o C C C C eq 1) C eq = 3/2 C 2) C eq = 2/3 C 3) C eq = 3 C 4) C eq = 1/3 C 5) C eq = 1/2 C What is the equivalent capacitance,, of the combination below? What is the equivalent capacitance, C eq, of the combination below?

33. ConcepTest 16.10bCapacitors II ConcepTest 16.10b Capacitors II 1) V 1 = V 2 2) V 1 > V 2 3) V 1 < V 2 4) all voltages are zero C 1 = 1.0  F C 3 = 1.0  F C 2 = 1.0  F 10 V How does the voltage V 1 across the first capacitor (C 1 ) compare to the voltage V 2 across the second capacitor (C 2 )?

34. ConcepTest 16.10bCapacitors II ConcepTest 16.10b Capacitors II 1) V 1 = V 2 2) V 1 > V 2 3) V 1 < V 2 4) all voltages are zero C 1 = 1.0  F C 3 = 1.0  F C 2 = 1.0  F 10 V The voltage across C 1 is 10 V. The combined capacitors C 2 +C 3 are parallel to C 1. The voltage across C 2 +C 3 is also 10 V. Since C 2 and C 3 are in series, their voltages add. Thus the voltage across C 2 and C 3 each has to be 5 V, which is less than V 1. How does the voltage V 1 across the first capacitor (C 1 ) compare to the voltage V 2 across the second capacitor (C 2 )? Follow-up: ? Follow-up: What is the current in this circuit?

35. ConcepTest 16.10cCapacitors III ConcepTest 16.10c Capacitors III C 1 = 1.0  F C 3 = 1.0  F C 2 = 1.0  F 10 V 1) Q 1 = Q 2 2) Q 1 > Q 2 3) Q 1 < Q 2 4) all charges are zero How does the charge Q 1 on the first capacitor (C 1 ) compare to the charge Q 2 on the second capacitor (C 2 )?

36. ConcepTest 16.10cCapacitors III ConcepTest 16.10c Capacitors III C 1 = 1.0  F C 3 = 1.0  F C 2 = 1.0  F 10 V Q = CVsame since V 1 > V 2 Q 1 > Q 2 We already know that the voltage across C 1 is 10 V and the voltage across both C 2 and C 3 is 5 V each. Since Q = CV and C is the same for all the capacitors, then since V 1 > V 2 therefore Q 1 > Q 2. 1) Q 1 = Q 2 2) Q 1 > Q 2 3) Q 1 < Q 2 4) all charges are zero How does the charge Q 1 on the first capacitor (C 1 ) compare to the charge Q 2 on the second capacitor (C 2 )?