Question

A long hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 12 a distributed uniformly across its cross section. a long wire which is coaxial with the cylinder carries an equal current in the same direction. what is the magnitude of the magnetic field 3.0 mm from the axis?

Answer 1

Here we can use ampere'a law to find the magnetic field

$\int B.dl = \mu_o i_{en}$

$B*2 \pi r = \mu_o (i_1 + \frac{i_2*\pi(3^2 - 2^2)}{\pi(4^2 - 2^2}$

$B*2 \pi*0.003 = 4\pi * 10^{-7} (12 + 5)$

$B = 4\pi * 10^{-7} (12 + 5)$

$B = 1.13 * 10^{-3} T$