A long tube of permanent-magnet material has inner radius

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

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

Problem

a = 8.0\,\mathrm{mm}

, outer radius

b = 12.0\,\mathrm{mm}

and length

50\,\mathrm{cm}

. The material is uniformly magnetised parallel to the tube's axis,

\mathbf{M} = M\hat{\mathbf{z}}

with

M = 5.0\times10^{5}\,\mathrm{A\,m^{-1}}

; the hollow bore (

s < a

) is empty, and no free current flows anywhere. Here

s

is the distance from the axis. The tube is long enough that, well away from the ends, each of its curved surfaces may be treated as the winding of an infinitely long solenoid. ((a)) Using

\mathbf{K}_b = \mathbf{M}\times\hat{\mathbf{n}}

, find the bound surface current per unit length on the outer curved surface and on the inner curved surface, stating the direction of each. Explain why there is no volume bound current. ((b)) By superposing the fields of the two equivalent solenoids, find the magnitude of

\mathbf{B}

inside the wall (

a < s < b

). ((c)) Find the magnitude of

\mathbf{B}

in the empty bore (

s < a

). ((d)) Find the magnitude of

\mathbf{B}

outside the tube (

s > b

Related theory

Magnetic materials

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