阿摩線上測驗
9. For electromagnetic waves propagating in conductors, we can derive the modified wave equation: $$ \nabla^{2} \mathbf{E} - \mu \epsilon \frac{\partial^{2} \mathbf{E}}{\partial t^{2}} - \mu \sigma \frac{\partial \mathbf{E}}{\partial t} = 0 $$ Consider a monochromatic plane wave as $\mathbf{E} = \mathbf{E}_0 e^{i(kz - \omega t)}$, where the wave number $k$ is a complex number. Please derive the expression for the wave number $k$.
(A) $\omega \sqrt{\mu \epsilon} \left(1 + \frac{i\sigma}{\omega \epsilon}\right)^{\frac{1}{2}}$
(B) $i\omega \sqrt{\mu \epsilon} \left(1 + \frac{\sigma}{\omega \epsilon}\right)$
(C) $\omega \sqrt{\mu \epsilon} \left(1 + \frac{\omega \epsilon}{i\sigma}\right)^{1/2}$
(D) None of the above.
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統計： 尚無統計資料
統計： 尚無統計資料
