(a) Above the Curie temperature the Weiss molecular field adds to the applied field,…

PHYSICS · Subjective · 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) Above the Curie temperature the Weiss molecular field adds to the applied field, so the total field felt by a Curie-law paramagnet is

H+\lambda_W M

. Starting from the Curie law

M = \dfrac{C}{T}\left(H+\lambda_W M\right)

, with

C

the Curie constant and

\lambda_W

the Weiss constant, derive the Curie-Weiss law

\chi_m = \dfrac{C}{T-T_C}

and show that

T_C = \lambda_W C

. (b) A small element of magnetic material sits inside a long solenoid of

N

turns, held at constant current

I

, and is free to move a small distance

\delta x

along the axis, changing the circuit's self-inductance from

L

L+\delta L

. The stored energy is

U(x,I) = \tfrac12 L(x) I^2

, and the flux linkage of the winding is

\Lambda = N\Phi = L(x)I

(a linear system, so

L

does not depend on

I

). Using the fact that, at constant current, the source must supply work

I\,\delta\Lambda

against the back-emf as

x

changes, derive the virtual-work rule

F = +\left.\dfrac{\partial U}{\partial x}\right|_I

for the mechanical force on the element, and state the corresponding rule at fixed flux linkage

\Lambda

instead.

Related theory

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