Paul A Tipler Gene Mosca Physics for Scientists

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

21 -1 Electric Charge 2

Electric Charge Q = ± Ne, (N = integer) Charge of Matter qproton = +e qneutron = 0 qelectron = -e Examples: He = (2 p, 2 n, 2 e-) charge = 0 He+ = (2 p, 2 n, 1 e-) = +1 e 3

Charge Interaction Like charges repel Unlike charges attract 4

Relative affinity of materials in attracting electrons. 5

21 -2 Conductors and Insulators 6

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

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

Charging by Induction (1 of 3) 9

Charging by Induction (2 of 3) 10

Charging by Induction (3 of 3) 11

attraction of an uncharged conductor 12

“Ground” = source or sink of charge 13

Charge re-distributes quickly after rod moves far away 14

21 -3 Coulomb’s Law 15

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Example in 2 D 17

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

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Direction of E 20

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

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. r 1/r 1 = {(6, 2) – (1, 0)}/ (29). = (5, 2)/ (29) r 2/r 2 = (3, 2)/ (13) r 3/r 3 = (1, 2)/ (5) 22

Components of Total Electric Field 23

The net electric field at (6, 2) is E = E 1 + E 2 + E 3. E = kq(0. 1855, 0. 2344) angle of E = tan-1(. 2344/. 1855) = 51. 6. magnitude of E = kq (0. 18552 + 0. 23442) = 0. 2989 kq= 0. 2989 k. Q/3 = 0. 09963 k. Q The exact value of E = k. Q/12 = 0. 08333 k. Q 24

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

Electric Field around a Dipole 26

21 -5 Electric Field Lines 27

Effect of point charge on oil soaked threads 28

Electric Field Lines (EFLs) inferred from experiment 29

Effect of two like point charges on oil soaked threads 30

Electric Field Lines (EFLs) inferred from experiment 31

Effect of two unlike point charges on oil soaked threads 32

Electric Field Lines (EFLs) inferred from experiment 33

EFL Conventions 34

EFLs lines for +q as distance from charges increas 35

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

21 -6 Motion of Point Charges in Electric Fields 37

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Force on – charge is opposite to E. 39

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21 -7 Electric Dipoles in Electric Fields 41

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Problems 43

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