This problem has two independent parts: one translates the Weiss self-consistency…

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

This problem has two independent parts: one translates the Weiss self-consistency condition into a graphical solution, the other translates a described hysteresis loop into its standard parameters. ((a)) At a temperature T=0.8 TCT = 0.8\,T_C, the Weiss self-consistency condition at zero applied field is L(x)=T3TCxL(x) = \dfrac{T}{3T_C}x, where xx is the usual scaled variable and L(x)=coth⁡x−1/xL(x) = \coth x - 1/x is the Langevin function. Data: L(1.80)=0.501L(1.80)=0.501, L(1.90)=0.520L(1.90)=0.520, L(2.00)=0.537L(2.00)=0.537, L(2.10)=0.554L(2.10)=0.554, L(2.20)=0.570L(2.20)=0.570. By plotting (or tabulating) L(x)L(x) against the straight line T3TCx\dfrac{T}{3T_C}x for T=0.8TCT=0.8T_C, find the non-zero crossing and state M/MsM/M_s to two significant figures. ((b)) A published hysteresis loop for a soft ferrite core is described as follows: on increasing HH, the loop saturates at Bs=0.40 TB_s = 0.40\,\mathrm{T}; on then decreasing HH back to zero, BB falls to 0.35 T0.35\,\mathrm{T}; continuing to negative HH, the upper branch crosses B=0B=0 at H=−12 A m−1H=-12\,\mathrm{A\,m^{-1}}. Read off the saturation flux density, the remanence and the coercivity.

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