A magnetic field H is applied to a material with a positive susceptibility χ . Assume M // H and that the M versus H plot is linear with a slope χ (Figure 2.5a).

a. Determine the work done when H varies from zero to $H = H_f$ .

b. Sketch the area on the H – M plot that corresponds to the work done on the material.
c. The product of $V_{\mu _{0}} , M_f · H_f$ , is an energy. Subtract your answer in part (a) from the value $M_f \cdot H_f$ . What is this energy?

Question

A magnetic field H is applied to a material with a positive susceptibility χ . Assume M // H and that the M versus H plot is linear with a slope χ (Figure 2.5a).

a. Determine the work done when H varies from zero to [latex] H = H_f [/latex].

b. Sketch the area on the H – M plot that corresponds to the work done on the material.
c. The product of [latex] V_{\mu _{0}} , M_f · H_f [/latex] , is an energy. Subtract your answer in part (a) from the value [latex] M_f · H_f [/latex] . What is this energy?

Accepted Answer

a. [latex]w = V\mu_{0} \int_{0}^{M_{f}}{H} dM = V\mu_{0} \int_{0}^{M_{f} }{\frac{M}{\chi } }dM=\frac{V\mu_{0} M^{2}_{f} }{2\chi } =\frac{V\mu_{0} M_f H_f}{2}[/latex]

b. Refer to Figure 2.5b.

c. This is the work that the moments, M , performed against the applied magnetic field, H , in resisting magnetization. Since this was a reversible and linear process, the work is equal to in magnitude and opposite in sign to the work applied to the material.

Question 2.12.2: A magnetic field H is applied to a material with a positive ...

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