Question

A conductor is made in the form of a hollow cylinder with inner and outer radii a and b, respectively. It carries a current I, uniformly distributed over its crosssection. Derive expressions for the magnitude of the magnetic field in the regions
a) r < a
b) a < r
c) r > b

Answer 1

a) If r <a then

        I_encl = 0 so B = 0

b) a<r

The current enclosed is

      Iencl = I [ A _a-->r / A _a-->b ]

             =I [ π( r² -a² ) / π(b²-a²) ]

        ∫ B .dl =μ_o I_encl

          B (2π r ) = μ_o I [ π( r²-a² ) / π(b² -a²)]

           B =( μ_o I/ 2 π r  )[ π(r² -a² ) / π(b²-a²) ]

c) when r>b then I_encl = I  

       B =(μ_o I/ 2 π r  )