An infinitely long, thick cylindrical shell of inner radius a and outer radius b carries a current I uniformly distributed across a cross section of the shell. 

(a) On a sketch of a cross section of the shell, draw some magnetic field lines. The current flows out of the page. Consider all regions (r ≤ a, a ≤ r ≤ b, b ≤ r). 

(b) Sketch a graph of the magnetic field magnitude as a function of r. 

(c) Find the magnetic field for r > b.

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al (b)