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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

Figure CQ19.7 shows a coaxial cable carrying current I in its inner conductor and a return current of the same magnitude in the opposite direction in the outer conductor. The magnetic field strength at r = r0 is Find the ratio B/B0, at (a) r = 2r0 and (b) r = 4r0.

images

Figure CQ19.7

a)

To determine
The ratio BB0 at r=2r0 .

Explanation

Given info: The current in the inner conductor is I . The current in the outer conductor is in the opposite direction with same magnitude. For r=r0 the magnetic field is B0 .

Explanation:

The Amperes circuital law can be written as,

BΔl=μ0I

Segment of a closed path

B is the component of B parallel to the segment of length Δl

I is the current enclosed in the closed path

μ0 is the permeability of free space

For the circular path with r=r0 , the current enclosed inside the path is I . Hence using the Ampere law,

B0(2πr0)=μ0IB0=μ0I2πr0       (1)

For the circular path with r=2r0 , the current enclosed inside the path is I

b)

To determine
The ratio BB0 at r=4r0 .

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