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Physics for Scientistsand Engineers

Chapter 21:The Electric Field I:

Discrete Charge Distributions

Copyright © 2004 by W. H. Freeman & Company

Paul A. Tipler • Gene Mosca

Fifth Edition

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21-1Electric Charge

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Electric Charge

Q = ± Ne, (N = integer)

Charge of Matter

qproton = +e qneutron = 0 qelectron = -e

Examples:

He = (2p, 2n, 2e-) charge = 0

He+ = (2p, 2n, 1e-) = +1e

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Charge Interaction

Like charges repelUnlike charges attract

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Relative affinity of materials

in attracting electrons.

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21-2Conductors and Insulators

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Conductors

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

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

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Charging by Induction (1 of 3)

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Charging by Induction (2 of 3)

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Charging by Induction (3 of 3)

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attraction of an uncharged conductor

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“Ground” = source or sink of charge

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Charge re-distributes quickly after rod moves far away

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21-3Coulomb’s Law

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Example in 2D

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Electric Field

force per charge-size [N/C]

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Direction of E

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Electric Field of a Point Charge

Electric Field due to Multiple Point Charges

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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)

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)01281.0,03202.0()29(

)2,5(33

1

1

1

12

11 kq

kq

r

rkq

r

r

r

kqE

)04267.0,06400.0()13(

)2,3(233

2

2

2

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22 kq

kq

r

rkq

r

r

r

kqE

)1789.0,08944.0()5(

)2,1(233

3

3

3

32

33 kq

kq

r

rkq

r

r

r

kqE

Components of Total Electric Field

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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(0.18552 + 0.23442) = 0.2989kq= 0.2989kQ/3 = 0.09963kQ

The exact value of E = kQ/12 = 0.08333kQ

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

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Electric Field around a Dipole

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21-5Electric Field Lines

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Effect of point charge on oil soaked threads

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Electric Field Lines (EFLs) inferred from experiment

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Effect of two like point charges on oil soaked threads

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Electric Field Lines (EFLs) inferred from experiment

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Effect of two unlike point charges on oil soaked threads

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Electric Field Lines (EFLs) inferred from experiment

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EFL Conventions

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EFLs lines for +q as distance from charges increas

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Relative charge = #lines leaving – #lines entering

Example:

Each sphere has count of +8

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21-6Motion of Point Charges in

Electric Fields

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Force on – charge is opposite to E.

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21-7Electric Dipoles in

Electric Fields

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Problems

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