Question

Derive the expression for alpha and beta in a conduction medium

Answer 1

Answer:

Propagation in Conductors

A so-called Ohmic conductor is a medium that satisfies Ohm's law, which can be written in the form

$\displaystyle {\bf j} = \sigma {\bf E},$ (862)

where $ {\bf j}$ is the current density (i.e., the current per unit area), $ {\bf E}$ the electric field-strength, and $ \sigma$ a constant known as the electrical conductivity of the medium in question. The $ z$ -directed propagation of a plane electromagnetic wave, linearly polarized in the $ x$ -direction, through an Ohmic conductor of conductivity $ \sigma$ is governed by (see Appendix C)

$\displaystyle \frac{\partial E_x}{\partial t} +\frac{\sigma}{\epsilon_0} E_x$ $\displaystyle =-\frac{1}{\epsilon_0}\, \frac{\partial H_y}{\partial z},$ (863)

$\displaystyle \frac{\partial H_y}{\partial t}$ $\displaystyle = - \frac{1}{\mu_0} \frac{\partial E_x}{\partial z},$ (864)