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A coaxial cable consists of a solid inner conductor of radius a , surrounded by a concentric cylindrical tube of inner radius b and outer radius c . The conductors carry equal and opposite currents I_0 distributed uniformly across their cross-sections.

(a) Determine the magnitude and direction of the magnetic field at a distance r from the axis.

   (i) r<a
   (ii) a<r<b

 

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Sadha
SadhaLv10
23 Mar 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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A coaxial cable consists of a solid inner conductor of radius R1 surrounded by a concentric cylindrical tube of inner radius R2and outer radius R3 (the figure). The conductors carry equal and opposite currents I0 distributed uniformly across their cross-sections. (Figure 1)

Figure 1: 

Part A

Determine the magnetic field at a distance R from the axis for R<R1.

Express your answer in terms of some or all of the variables R, R1, R2, R3, I0, and appropriate constants.

Part B

Determine the magnetic field at a distance R from the axis for R1<R<R2.

Express your answer in terms of some or all of the variables R, R1, R2, R3, I0, and appropriate constants.

Part C

Determine the magnetic field at a distance R from the axis for R2<R<R3.

Express your answer in terms of some or all of the variables R, R1, R2, R3, I0, and appropriate constants.

Part D

Determine the magnetic field at a distance R from the axis for R>R3.

Express your answer in terms of some or all of the variables R, R1, R2, R3, I0, and appropriate constants.

A very long coaxial cable consists of a solid cylindrical innerconductor of radius {R1} surrounded by an outer cylindricalconductor with inner radius {R2} and outer radius {R3}. The regionbetween the two conductors is filled with a waxlike insulatingmaterial to keep the conductors from touching each other.
Part A -
If the inner and outer conductors carry equal currents I inopposite directions, use Ampère's law to derive an expression forthe magnetic field as a function of r (the distance from thecentral axis) at points between the two conductors({R1}<r<{R2}).
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If the inner and outer conductors carry equal currents I inopposite directions, use Ampère's law to derive an expression forthe magnetic field as a function of r (the distance from thecentral axis) at points outside the cable (r>{R3}).
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