A hypothetical alloy X obeys the Weiss molecular-field model above its Curie temperature

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Condensed Matter, Materials & Soft Matter · Magnetic materials

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

Problem

A hypothetical alloy X obeys the Weiss molecular-field model above its Curie temperature, with Curie constant

C = 1.0\,\mathrm{K}

and molecular-field constant

\lambda_W = 1040

(dimensionless). ((a)) Starting from

M = (C/T)(H + \lambda_W M)

, derive the Curie-Weiss law

\chi_m = C/(T - T_C)

and an expression for

T_C

in terms of

C

and

\lambda_W

. Evaluate

T_C

for alloy X. ((b)) A long rod of alloy X, held at

T = 1300\,\mathrm{K}

(above

T_C

), sits inside a long solenoid that produces

H = 1.0\times10^5\,\mathrm{A\,m^{-1}}

along the rod. Using the Curie-Weiss susceptibility from part (a), derive the work done per unit volume by the solenoid's current source in raising the field in the rod from

H=0

to this final value, and evaluate it. (Treat the rod as a linear magnetic medium at this fixed

T

.) ((c)) The rod has cross-sectional area

S = 3\,\mathrm{cm^2}

, with one end well inside the solenoid and the other well outside. Using virtual work at constant current, derive the inward force pulling the rod in, and evaluate it at the field of part (b).

Related theory

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