A toroidal core of a soft iron alloy is operated in the linear (unsaturated) part of…

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

The Boundary-Value Problem, Ch Ferromagnetism: the Weiss field, domains, hysteresis and the magnetic circuit

Problem

A toroidal core of a soft iron alloy is operated in the linear (unsaturated) part of its magnetisation curve, where the relative permeability is

\mu_r = 1200

. A steady auxiliary field

H = 600\,\mathrm{A\,m^{-1}}

is set up in the core by its winding. ((a)) Find

B

in the core, and the work done per unit volume by the winding's source in driving it from

H=0

up to this value, treating the response as linear over this range. ((b)) The core's full hysteresis loop (measured separately, at a larger drive) saturates at

B_s = 1.8\,\mathrm{T}

; when

H

is then brought back to zero,

B

falls to

1.0\,\mathrm{T}

, and a reversed field of

40\,\mathrm{A\,m^{-1}}

brings

B

to zero. Give the remanence and the coercivity, and say what each means physically. ((c)) The full loop encloses an area (energy dissipated per cycle) of

150\,\mathrm{J\,m^{-3}}

. For a core of volume

0.02\,\mathrm{m^3}

driven at

50\,\mathrm{Hz}

, find the power dissipated as heat.

Related theory

Magnetic materials

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