1 Physics for Scientists and Engineers Chapter 23: Electric Potential Copyright © 2004 by W. H. Freeman & Company Paul A. Tipler Gene Mosca Fifth Edition

2 Electric Potential V V ~ energy per unit charge for motion Total energy to move charge q is “U” = qV useful since V is often constant

3 Definitions V ~ U/q ~ FL/q ~ (F/q)L ~ EL

4 Energy

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6 Inferring V from E

Potential Due to a System of Point Charges

8 Work done by the electric field depends on direction of motion.

9 Checkpoint (In this part of the class) force = Eq

10 Potential is defined equal to a Change In Potential, …relative to a reference position. r ref is arbitrary and is the location where V = 0. Frequently the reference position is infinity, i.e. far from all charges.

11  Energy = charge x  potential Energy needed to move a charge from infinity to r is called U.

12 Work done by push may be opposite of work done by field work done by the field in this diagram is negative this causes  U to be positive

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14 Remember Change in Energy has opposite sign of work done e.g. Engine does positive work in accelerating car, Energy (fuel-level) decreases.

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Computing the Electric Field From the Potential

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Calculations of V for Continuous Charge Distributions

20 Potential is a Scalar Integral which is an easier calculation than E which is a Vector Integral

21 All charge at distance r.

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23 dq dV V

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25 If x >> R: which is a point-charge potential

26 If x << R: Potential approaches finite value the Potential is not the same function as found for an infinite plane of charge since V ≠ 0 when r = infinity but… This limit would work for E since charges at large distances would have a canceling effect on E, due to the vector addition.

27 xV

28 For infinite charge distributions the potential must be set = 0 at a finite distance from the charges. This causes the potential function to approach –infinity as x  infinity.

29 Returning to Spherical Charge Distributions…

30 E = 0 inside a conducting shell implies V = constant inside

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Equipotential Surfaces

33 Example Equi-Potential

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35 Problems

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41 Potential of Point Charge in Spherical Shell

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