A coaxial cable consists of a solid inner conductor of radius and a thin cylindrical…

PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Magnetic Fields and Electromagnetism · Magnetic Fields and Electromagnetism

Problem

A coaxial cable consists of a solid inner conductor of radius

a

and a thin cylindrical outer conductor of radius

b\,(>a)

. The inner conductor carries a steady current

I

directed out of the page, while the outer conductor carries an equal current

I

directed into the page, uniformly distributed over its surface. (i) Derive expressions for the magnetic field magnitude

B(r)

in the following regions: (A)

0<r<a

, (B)

a<r<b

, (C)

r>b

. (ii) Draw a qualitative sketch of

B

versus

r

from the axis (

r=0

) to

r=2b

. (iii) For

a=2\,\text{mm}

b=10\,\text{mm}

and

I=15\,\text{A}

, calculate

B

at (a)

r=1\,\text{mm}

, (b)

r=6\,\text{mm}

and (c)

r=20\,\text{mm}

. Express each answer in tesla.