Question

A long cylindrical wire of radius R, made from a linear material
with a magnetic susceptibility of X_{m} , 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 J_{b} and
K_{b} 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, J_{b,} and
K_{b)} Check that this is the same as your answer from part
a and b

Answer #1

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A free current I ﬂows uniformly in the z-direction down a long,
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