A solid conductor of radius R carrying current per unit area as J=br/R where b is a constant and r is the distance from axis. Find the magnetic fields at a distance x:

x>R

x

αµR^2/3x is the magnetic field.

Explanation:

From ampere circuital law we get that the integration of B.ds will give us µ times current I enclosed.

So, in terms of current density we know that I enclosed will be J.dA so on integrating it we will get that the J is αr/R and the dA is 2πrdr.

Now for x>R we will get that dA is 2πxdx and the value of J is αx/R.

So, on integrating with substitution rule we will get the value of B to be αµR^2/3x where the value of ds while integration will be 2πx.