## Question

###### The scattering by the dielectric sphere of Problem $10.4$ was treated as purely electric dipole scattering. This is adequate unless it happens that the real dielectric constant $e / \epsilon_{0}$ is very large. In these circumstances a magnetic dipole contribution. even though higher order in $k R$, may be important. (a) Show that the changing magnetic flux of the incident wave induces an az. muthal current flow in the sphere and produces a magnetic dipole moment, $$ \mathrm{m}=\frac{i 4 \pi \si

The scattering by the dielectric sphere of Problem $10.4$ was treated as purely electric dipole scattering. This is adequate unless it happens that the real dielectric constant $e / \epsilon_{0}$ is very large. In these circumstances a magnetic dipole contribution. even though higher order in $k R$, may be important. (a) Show that the changing magnetic flux of the incident wave induces an az. muthal current flow in the sphere and produces a magnetic dipole moment, $$ \mathrm{m}=\frac{i 4 \pi \sigma Z_{0}}{k \mu_{0}}(k R)^{2} \frac{R^{3}}{30} \mathbf{B}_{\text {inc }} $$ (b) Show that application of the optical theorem to the coherent sum of the electric and magnetic dipole contributions leads to a total cross section, $$ \sigma_{i}=12 \pi R^{2}\left(R Z_{0} \sigma\right)\left[\frac{1}{\left(\epsilon_{r}+2\right)^{2}+\left(Z_{0} \sigma / k\right)^{2}}+\frac{1}{90}(k R)^{2}\right] $$