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A long cylindrical wire of radius R, made from a linear material with a magnetic susceptibility...

A long cylindrical wire of radius R, made from a linear material with a magnetic susceptibility of Xm , carries a volume current density J = ks ẑ along the z-axis.

For all below please include magnitude and direction:

(a) Find the auxiliary field H, the magnetic field B, and the magnetization M inside the wire

(b) Find the auxiliary field H, the magnetic field B, and the magnetization M outside the wire

(c) Find the bound current densities Jb and Kb of the wire, and show that the total current passing through the wire at any point is zero

(d) Calculate the magnetic field of B inside and outside the wire without invoking H or M (Hint: use J, Jb, and Kb) Check that this is the same as your answer from part a and b

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