Question

A long coaxial cable consists of two concentric conductors. The inner conductor is a cylinder with radius R_1, and it carries a current I_0 uniformly distributed over its cross section. The outer conductor is a cylindrical shell with inner radius R_2 and outer radius R_3. It carries a current I_0 that is also uniformly distributed over its cross section, and that is opposite in direction to the current of the inner conductor. Calculate the magnetic field {B} as a function of the distance R from the axis.

What is the direction and magnitude of the magnetic field for 0<r<R_1? Express your answer in terms of I_0, R_1, R_2, R_3, r and \mu _0 (enter mu_0 for \mu _0)

What is the direction and magnitude of the magnetic field for R_1<r<R_2? Express your answer in terms of I_0, R_1, R_2, R_3, r and \mu _0 (enter mu_0 for \mu _0)

What is the direction and magnitude of the magnetic field for R_2<r<R_3? Express your answer in terms of I_0, R_1, R_2, R_3, r and \mu _0 (enter mu_0 for \mu _0)

Answer 1

Use the Biot-Savart law: magnetic field do to an enclosed current.

a. enclosed current is proportonal to enclosed area, or 1/r^2
B=mu*Ienclosed/2PIr
but I enclosed=Io*r /R1^2
ans: B=mu*Io*r /R1^2
b. enclosed current is Io
B=mu*Io/2PI r

c. do the same as A, but you have to add (b) to it.
Enclosed current=Io-Io(r-R2)^2/(r-R3)^2
B=mu*Io(1-(r-R2)^2/(r-R3)^2 * 1/2PIr
check that.

Answer 2

a) and c) are wrong

Answer 3

part a) and c)are wrong !