# 1 Physics for Scientists and Engineers Chapter 21: The Electric Field I: Discrete Charge Distributions Copyright © 2004 by W. H. Freeman & Company Paul.

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1 Physics for Scientists and Engineers Chapter 21: The Electric Field I: Discrete Charge Distributions Copyright © 2004 by W. H. Freeman & Company Paul A. Tipler Gene Mosca Fifth Edition

2 21-1 Electric Charge

3 Electric Charge Q = ± Ne, (N = integer) Charge of Matter q proton = +e q neutron = 0 q electron = -e Examples: He = (2p, 2n, 2e - ) charge = 0 He + = (2p, 2n, 1e - ) = +1e

4 Charge Interaction Like charges repel Unlike charges attract

5 Relative affinity of materials in attracting electrons.

6 21-2 Conductors and Insulators

7 Conductors “free” electrons electron motion = “conduction”

8 Evidence of electron conduction away from central metallic element (gold leaf repulsion)

9 Charging by Induction (1 of 3)

10 Charging by Induction (2 of 3)

11 Charging by Induction (3 of 3)

12 attraction of an uncharged conductor

13 “Ground” = source or sink of charge

14 Charge re-distributes quickly after rod moves far away

15 21-3 Coulomb’s Law

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17 Example in 2D

18 Electric Field force per charge-size [N/C]

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20 Direction of E

21 Electric Field of a Point Charge Electric Field due to Multiple Point Charges

22 Example: Approximating E above Uniform Line of Charge Given: 6 m long uniform strip of charge Q lies along x axis 0, 6 m. Estimate E at P = (6, 2)m by breaking strip into 3 discrete point charges q = Q/3 located at 1, 3, and 5 m along the x-axis. r1/r1 = {(6, 2) – (1, 0)}/  (29). = (5,2)/  (29) r2/r2 = (3, 2)/  (13) r3/r3 = (1, 2)/  (5)

23 Components of Total Electric Field

24 The net electric field at (6,2) is E = E1 + E2 + E3. E = kq(0.1855, 0.2344) angle of E = tan-1(.2344/.1855) = 51.6 . magnitude of E = kq  (0.1855 2 + 0.2344 2 ) = 0.2989kq= 0.2989kQ/3 = 0.09963kQ The exact value of E = kQ/12 = 0.08333kQ

25 Dipole – two equal size opposite sign charges at small separation distance

26 Electric Field around a Dipole

27 21-5 Electric Field Lines

28 Effect of point charge on oil soaked threads

29 Electric Field Lines (EFLs) inferred from experiment

30 Effect of two like point charges on oil soaked threads

31 Electric Field Lines (EFLs) inferred from experiment

32 Effect of two unlike point charges on oil soaked threads

33 Electric Field Lines (EFLs) inferred from experiment

34 EFL Conventions

35 EFLs  lines for +q as distance from charges increas

36 Relative charge = #lines leaving – #lines entering Example: Each sphere has count of +8

37 21-6 Motion of Point Charges in Electric Fields

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39 Force on – charge is opposite to E.

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41 21-7 Electric Dipoles in Electric Fields

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43 Problems

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