1. ConcepTest 16.1Electric Charge I ConcepTest 16.1 Electric Charge I same charge The fact that the balls repel each other only can tell you that they have the same charge, but you do not know the sign. So they can be either both positive or both negative. 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? Follow-up: What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral?

2. negative neutral induction Clearly, the ball will be attracted if its charge is negative. However, even if the ball is neutral, the charges in the ball can be separated by induction (polarization), leading to a net attraction. 1) positive 2) negative 3) neutral 4) positive or neutral 5) negative or neutral A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be: remember the ball is a conductor! ConcepTest 16.2Conductors I ConcepTest 16.2 Conductors I Follow-up: What happens if the metal ball is replaced by a plastic ball?

3. positive charge will flow from the blue to the green ball due to polarization charges will remain on the separate conductors While the conductors are connected, positive charge will flow from the blue to the green ball due to polarization. Once disconnected, the charges will remain on the separate conductors even when the rod is removed. Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? ConcepTest 16.3Conductors II ConcepTest 16.3 Conductors II 1)00 2)+– 3)–+ 4)++ 5)– – 0 0 ? ? Follow-up: What will happen when the conductors are reconnected with a wire?

4. same magnitude force of one on the other of a pair is the same as the reverse Note that this sounds suspiciously like Newton’s 3rd Law!! The force F 2 must have the same magnitude as F 1. This is due to the fact that the form of Coulomb’s Law is totally symmetric with respect to the two charges involved. The force of one on the other of a pair is the same as the reverse. Note that this sounds suspiciously like Newton’s 3rd Law!! Q Q F 1 = 3N F 2 = ? 1) 1.0 N 2) 1.5 N 3) 2.0 N 4) 3.0 N 5) 6.0 N What is the magnitude of the force F 2 ? ConcepTest 16.4Coulomb’s Law I ConcepTest 16.4 Coulomb’s Law I

5. Originally we had: F before = k(Q)(Q)/d 2 = F Now we have: F after = k(Q)(Q)/(3d) 2 = 1/9 F 1) 9 F 2) 3 F 3) F 4) 1/3 F 5) 1/9 F The force between two charges separated by a distance d is F. If the charges are pulled apart to a distance 3d, what is the force on each charge? QF QFd Q?Q? 3d3d3d3d ConcepTest 16.5Coulomb’s Law III ConcepTest 16.5 Coulomb’s Law III Follow-up: What is the force if the original distance is halved?

6. APHY202 1/6/2016 6

7. APHY202 1/6/2016 7 17.1 Electric Potential Energy and Potential Difference   Review of work and energy   The electrostatic force is conservative. W = Fd = qEd PE b – PE a = -W

8. APHY202 1/6/2016 8 17.1 Electric Potential Energy and Potential Difference   The electric potential is the electric potential energy per unit charge.   Voltage

9. APHY202 1/6/2016 9 17.2 Electric Potential and Electric Field   If we have uniform electric field, then W = -qV ba and W = qEd   Therefore V ba = -Ed or   In general, the electric field is the rate at which the electric potential decreases over a distance.

10. APHY202 1/6/2016 10 17.3 Equipotential Lines

11. APHY202 1/6/2016 11 17.3 Equipotential Lines   No work is required to move along an equipotential line and E is perpendicular to the line.

12. APHY202 1/6/2016 12 17.4 The Electron Volt   The energy acquired by a charge ( ± e) after passing through a potential difference of 1 volt. 1 eV = 1.6 x 10 -19 J Lichtenberg Figures and Lightning

13. APHY202 1/6/2016 13 17.5 Electric Potential due to Point Charges   If V = 0 at r = ∞ then   The principle of superposition allows us to determine the potential due to multiple charges

14. APHY202 1/6/2016 14 17.5 Electric Potential due to Point Charges