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Download 17.5 Electric Potential due to Point Charges
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ConcepTest 16.1 Electric Charge I Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative 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. Follow-up: What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral? ConcepTest 16.2 Conductors I A metal ball hangs from the ceiling 1) positive by an insulating thread. The ball is 2) negative attracted to a positive-charged rod 3) neutral held near the ball. The charge of 4) positive or neutral the ball must be: 5) negative or neutral 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. remember the ball is a conductor! Follow-up: What happens if the metal ball is replaced by a plastic ball? ConcepTest 16.3 Conductors II Two neutral conductors are connected 1) 0 0 by a wire and a charged rod is brought 2) + – 3) – + 4) + + 5) – – near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? While the conductors are connected, positive 0 0 ? ? 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. Follow-up: What will happen when the conductors are reconnected with a wire? ConcepTest 16.4 Coulomb’s Law I What is the magnitude 1) 1.0 N 2) 1.5 N of the force F2? 3) 2.0 N F1 = 3N Q Q F2 = ? 4) 3.0 N 5) 6.0 N The force F2 must have the same magnitude as F1. 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!! ConcepTest 16.5 Coulomb’s Law III The force between two charges 1) 9 F separated by a distance d is F. If 2) 3 F the charges are pulled apart to a 3) F distance 3d, what is the force on 4) 1/3 F each charge? 5) 1/9 F F Originally we had: F Q Q Fbefore = k(Q)(Q)/d2 = F Now we have: Fafter = k(Q)(Q)/(3d)2 = 1/9 F d ? ? Q Q 3d Follow-up: What is the force if the original distance is halved? 5/25/2017 APHY202 6 17.1 Electric Potential Energy and Potential Difference Review of work and energy The electrostatic force is conservative. W = Fd = qEd PEb – PEa = -W 5/25/2017 APHY202 7 17.1 Electric Potential Energy and Potential Difference The electric potential is the electric potential energy per unit charge. PEa Va q 5/25/2017 Voltage PEb PEa Vba q APHY202 8 17.2 Electric Potential and Electric Field 5/25/2017 If we have uniform electric field, then W = -qVba and W = qEd Therefore Vba = -Ed or Vba E d In general, the electric field is the rate at which the electric potential decreases over a distance. APHY202 9 17.3 Equipotential Lines 5/25/2017 APHY202 10 17.3 Equipotential Lines 5/25/2017 No work is required to move along an equipotential line and E is perpendicular to the line. APHY202 11 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 5/25/2017 APHY202 12 17.5 Electric Potential due to Point Charges If V = 0 at r = ∞ then Q V k r 5/25/2017 The principle of superposition allows us to determine the potential due to multiple charges APHY202 13 17.5 Electric Potential due to Point Charges 5/25/2017 APHY202 14