Question

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

Answer 1

We can use Ampere's law to find the magnetic field

$$\int Bdl=\mu_0 i_{en}$$

$$2\pi rB=\mu_0\left(i_1+i_2\frac{\pi(3^2-2^2)}{\pi(4^2-2^2)}\right)$$

$$2\pi (0.003)B=4\pi\cdot10^{-7}\left(12+5\right)$$

$$B=1.1\cdot 10^{-3}T=1.1\ mT$$