Question

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

• A. $\frac{\epsilon {\epsilon }_o\omega }{\sigma }$
• B. $\frac{\sigma }{\epsilon {\epsilon }_o\omega }$
• C. $\frac{\omega }{\sigma {\epsilon }_0\epsilon }$
  
• D. $\frac{\omega \sigma }{{\epsilon }_0\epsilon }$

Answer 1

The correct option is B $\frac{\sigma }{\epsilon {\epsilon }_o\omega }$

Conduction current density $J_c=\sigma E_{0}sin(\omega t-kx)\text{displacement current}{i}_d=\epsilon {\epsilon }_o\frac{d{\varphi }_E}{dt}=\epsilon {\epsilon }_{o}A\frac{dE}{dt}=\epsilon {\epsilon }_o\times A{E}_0\omega cos(\omega t-kx)\text{displacement current density}{J}_d=\epsilon {\epsilon }_o{E}_0\omega \Rightarrow \frac{J_c}{J_d}=\frac{\sigma }{\epsilon {\epsilon }_o\omega }$