A plane electromagnetic wave of angular frequ | vedclass

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(B) The conduction current density is given by $J_c = \sigma E$,where $E = E_0 \sin(\omega t - kx)$. Thus,the magnitude is $J_c = \sigma E_0$.The disp

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$\frac{\sigma}{\varepsilon \varepsilon_0 \omega}$

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(B) The conduction current density is given by $J_c = \sigma E$,where $E = E_0 \sin(\omega t - kx)$. Thus,the magnitude is $J_c = \sigma E_0$.The displacement current density is given by $J_d = \varepsilon \varepsilon_0 \frac{\partial E}{\partial t}$.Since $E = E_0 \sin(\omega t - kx)$,we have $\frac{\partial E}{\partial t} = E_0 \omega \cos(\omega t - kx)$.Thus,the magnitude of displacement current density is $J_d = \varepsilon \varepsilon_0 E_0 \omega$.The ratio of conduction current density to displacement current density is $\frac{J_c}{J_d} = \frac{\sigma E_0}{\varepsilon \varepsilon_0 E_0 \omega} = \frac{\sigma}{\varepsilon \varepsilon_0 \omega}$.

$A$ plane electromagnetic wave of angular frequency $\omega$ propagates in a poorly conducting medium of conductivity $\sigma$ and relative permittivity $\varepsilon$. Find the ratio of conduction current density and displacement current density in the medium.

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