A long solid cylindrical conductor of radius carries a total current that is…

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

Problem

A long solid cylindrical conductor of radius

a

carries a total current

I

that is uniformly distributed over its cross-section. (i) Obtain an expression for the magnetic field magnitude

B(r)

inside the conductor for

0<r<a

. (ii) Obtain an expression for

B(r)

outside the conductor for

r\ge a

. (iii) Sketch qualitatively the variation of

B

with

r

from the centre (

r=0

) to

r=2a

. (iv) For

a=5\,\text{mm}

and

I=10\,\text{A}

, calculate

B

at (a)

r=3\,\text{mm}

and (b)

r=1\,\text{cm}

. Express each answer in tesla.