Question

A long coaxial cable consists of two concentric conductors. The inner conductor is a cylinder with radius R1, and it carries a current I0 uniformly distributed over its cross section. The outer conductor is a cylindrical shell with inner radius R2 and outer radius R3. It carries a current I0 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.

a)find magnitude of the magnetic field for 0 < r < R1

b)Find magnetic field for R1 < r < R2

c)find magnitude of the magnetic field for R2 < r < R3

Answer 1

a)(mu_0*I_0*r)/(2*pi*R_1^2)
b)(mu_0*I_0)/(2*pi*r)
c)(mu_0*I_0*(R_3^2-r^2))/(2*pi*r*(R_3^2-R_2^2))