A hypothetical alloy Y is studied 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 Y is studied above its Curie temperature. A plot of

1/\chi_m

against

T

is a straight line of slope

1.0\,\mathrm{K^{-1}}

that crosses the temperature axis at

1080\,\mathrm{K}

, and well below that temperature the alloy saturates at

M_s = 1.6\times10^6\,\mathrm{A\,m^{-1}}

. Treat the alloy with the Weiss model and the classical Curie constant

C = \mu_0N_vm^2/3k_B

. ((a)) Find

C

, the model's

T_C

and

\lambda_W

. ((b)) Using

M_s = N_vm

together with

C

, find the moment per atom

m

, in units of the Bohr magneton

\mu_B = 9.274\times10^{-24}\,\mathrm{J\,T^{-1}}

, and the number density

N_v

of moments. ((c)) Find the Weiss field

\mu_0\lambda_WM_s

and compare it with the field

\mu_0H

of a laboratory solenoid producing

H = 8.0\times10^4\,\mathrm{A\,m^{-1}}

. ((d)) A long rod of alloy Y, of cross-section

S = 5\,\mathrm{cm^2}

and held at

T = 1500\,\mathrm{K}

, lies along the axis of that solenoid, driven at constant current, with one end well inside and the other well outside. Find the force drawing it in.

Related theory

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