A closed ring of soft ferrite (

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

The Boundary-Value Problem, Ch Magnetisation, bound currents and H, completed

Problem

\mu_r = 800

, treated as linear) has mean circumference

L = 0.20\,\mathrm{m}

and a cross-section small compared with

L

. It is wound uniformly with

N = 200

turns carrying

I = 0.10\,\mathrm{A}

. A narrow gap of width

g = 1.0\,\mathrm{mm}

is then cut straight across the ring. Take the gap to be narrow enough that

\mathbf{B}

crosses it without spreading, so that

B

has the same value all the way round the loop. ((a)) Before the gap is cut, find

B

in the ring. ((b)) With the gap, find

H

in the ferrite,

H

in the gap and

B

in the gap. ((c)) Let

H_0 = NI/L

be the field the winding alone would set up if free current were the only source of

\mathbf{H}

. Show that the gapped ring obeys

H_{\rm ferrite} = H_0 - N_{\rm eff}M

exactly, find

N_{\rm eff}

in terms of

g

and

L

, and find the apparent susceptibility

\chi_{\rm app} = M/H_0

of the gapped ring. ((d)) Explain, in terms of the surface term

\mathbf{M}\cdot\hat{\mathbf{n}}

, how a gap only one two-hundredth of the circumference can cut

B

by a factor of five.