Question

A hollow conducting tube of radius R carries a current 5I down its length. Determine an expression for the magnetic field inside and outside the tube (for both r<R and r>R)

Answer 1

According to the Ampere's law
   
Now for cylindrical symmetry, and for the current flowing along the z axis, we have the magnetic field
   
And so,
   
Now for a circular loop or radius r, we have
  
  
  
Now for r < R, we have for the hollow cylinder of radius R,

And so,
   

And for r > R, the enclosed current is given by
  
And so,