1. 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. 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. 3 Definitions V ~ U/q ~ FL/q ~ (F/q)L ~ EL

4. 4 Energy

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6. 6 Inferring V from E

7. 7 23-2 Potential Due to a System of Point Charges

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

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

10. 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. 11  Energy = charge x  potential Energy needed to move a charge from infinity to r is called U.

12. 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. 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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17. 17 23-3 Computing the Electric Field From the Potential

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19. 19 23-4 Calculations of V for Continuous Charge Distributions

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

21. 21 All charge at distance r.

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23. 23 dq dV V

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

26. 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. 27 xV 10.414214 20.236068 30.162278 40.123106 50.09902 60.082763 70.071068 80.062258 90.055385 100.049876 110.045361 120.041595 130.038405 140.035669 150.033296 160.03122 170.029386

28. 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. 29 Returning to Spherical Charge Distributions…

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

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32. 32 23-5 Equipotential Surfaces

33. 33 Example Equi-Potential

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35. 35 Problems

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41. 41 Potential of Point Charge in Spherical Shell

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