A long straight non-magnetic wire of radius carries a steady free current

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetic materials

Electricity, Magnetism and Electromagnetism, Ch Magnetisation, bound currents and the auxiliary field H

Problem

A long straight non-magnetic wire of radius

a = 1.0\,\mathrm{mm}

carries a steady free current

I = 12\,\mathrm{A}

, distributed uniformly over its cross-section and flowing in the direction we call

+z

. Coaxial with the wire is a long thick tube of a linear magnetic material of relative permeability

\mu_r = 300

, with inner radius

b = 2.0\,\mathrm{mm}

and outer radius

c = 5.0\,\mathrm{mm}

. The gap between wire and tube, and everything outside the tube, is empty space. The arrangement is long enough that end effects are ignored, and

s

denotes the perpendicular distance from the axis. Find: ((a)) the magnitude of

\mathbf{H}

s = 3.0\,\mathrm{mm}

; ((b)) the magnitude of

\mathbf{B}

there; ((c)) the magnitude of

\mathbf{M}

there; ((d)) the bound surface current per unit length on the inner surface (

s = b

) and on the outer surface (

s = c

) of the tube, with the direction of each; ((e)) the total bound current flowing along the inner surface of the tube.