Consider the following model of a coaxial cable An inner con

Consider the following model of a coaxial cable: An inner conductor of radius  a carries a current  I into the page; this current is evenly distributed through the conducting cyliner. An outer conducting shell (inner radius b , outer radius c ) carries a current I out of the page. A diagram of this is shown below:

Part A

What is the current density in the inner cylinder?

Call the current positive if it is in the  +k^ direction and negative if it is in the  ?k^ direction.

Part B

What is the current density in the outer conducting hollow cylinder?

Call the current positive if it is in the  +k^ direction and negative if it is in the  ?k^ direction.

Part C

Inside the cable (for r<a ), does the magnetic field go around clockwise or counterclockwise? (Or is there no field?)

Part D

What is the magnitude of the magnetic field inside the cable (that is, for r<a ), as a function r of distance from the center?

Part E

In between the two conductors ( a<r<b ), does the magnetic field go around clockwise or counter clockwise? Or is it zero?

Part F

In between the cylinders ( a<r<b ), what is the magnitude of the magnetic field, as a function of r ?

Part G

In the outer shell ( b<r<c ), does the magnetic field go around clockwise or counterclockwise? (Or is it zero?)

Part H

In the outer cylinder ( b<r<c ), what is the magnitude of the magnetic field?

Part I

Outside the entire cable ( r>c ), what direction is the magnetic field? Or is it zero?

Solution

a)

current density,

J 1= I/A = I/pi*a^2

b)

Current density outside is,

J2= I/pi(c^2 - b^2)

c)

Counter clock wise direction

d)

From ampere\'s law,

B*2*pi*r = mu*J*pi*r^2

= mu*I*pi*r^2/pi*a^2
B = mu*I*r/2*pi*a^2