Question

In: Physics

A conductor is made in the form of a hollow cylinder with innerandouter radii a...

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

Solutions

Expert Solution

a) If r <a then
        Iencl = 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 =μo Iencl
          B (2π r ) = μo I [ π( r2-a2 ) / π(b2 -a2)]
           B =( μo I/ 2 π r  )[ π(r2 -a2 ) / π(b2-a2) ]
c) when r>b then Iencl = I  
       B =(μo I/ 2 π r  )
   

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