Chapter 8, Problem 29P

(a)

To determine

Prove that the boundary conditions on the magnetization vector are $\frac{M_{1t}}{{\chi }_{m1}}-\frac{M_{2t}}{{\chi }_{m2}}=K$ and $\frac{{\mu }_1}{{\chi }_{m1}}{M}_{1n}=\frac{{\mu }_2}{{\chi }_{m2}}{M}_{2n}$.

(b)

To determine

Prove that if the boundary is not current free then $\frac{\tan {\theta }_1}{\tan {\theta }_2}=\frac{{\mu }_1}{{\mu }_2}\left[1+\frac{K{\mu }_2}{B_2\sin {\theta }_2}\right]$.