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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 22 / Problem 20E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Answer: (a) At a distance of 0.200 cm from the center of a

Chapter 22, Problem 20E

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QUESTION:

Problem 20E

(a) At a distance of 0.200 cm from the center of a charged conducting sphere with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the center of the sphere? (b) At a distance of 0.200 cm from the axis of a very long charged conducting cylinder with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the axis of the cylinder? (c) At a distance of 0.200 cm from a large uniform sheet of charge, the electric field is 480 N/C. What is the electric field 1.20 cm from the sheet?

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QUESTION:

Problem 20E

(a) At a distance of 0.200 cm from the center of a charged conducting sphere with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the center of the sphere? (b) At a distance of 0.200 cm from the axis of a very long charged conducting cylinder with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the axis of the cylinder? (c) At a distance of 0.200 cm from a large uniform sheet of charge, the electric field is 480 N/C. What is the electric field 1.20 cm from the sheet?

ANSWER:

Solution 20E

The magnitude of electric field at a distance $r$ from the center of a conducting sphere with a charge $q$ is given by $E=\frac{q}{4\pi{}\epsilon{}{\ }_{0}r{\ }^{2}}$ .

(a) Given, electric field $E=480\ N/C$

Distance $r=0.200\ cm=0.200\times{}1{0}^{-2}\ m$

$480=\frac{q}{4\pi{}\epsilon{}{\ }_{0}\times{}(0.200\times{}1{0}^{-2}{)}^{2}}$

$q=480\times{}4\pi{}\epsilon{}{\ }_{0}\times{}(0.200\times{}1{0}^{-2}{)}^{2}\ C$

$q=480\times{}4\times{}3.14\times{}8.85\times{}1{0}^{-12}\times{}0.04\times{}1{0}^{-4}\ C$

$q=2134\times{}1{0}^{-16}\ C$

$q=2.134\times{}1{0}^{-13}\ C$

Therefore, the electric field from 0.600 cm from the center of the sphere is,

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