A plane electromagnetic wave of angular frequency propagates in a… - Vidyadip

MCQ

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.

A
$\frac{\varepsilon \varepsilon_0 \omega}{\sigma}$
✓
$\frac{\sigma}{\varepsilon \varepsilon_0 \omega}$
C
$\frac{\omega}{\sigma \varepsilon \varepsilon_0 }$
D
$\frac{\omega \sigma}{ \varepsilon \varepsilon_0 }$

✓

Answer

Correct option: B.

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

b
$J_{c}=\sigma E_{0} \sin (\omega t-k x)$

${{\text{i}}_{\text{d}}} = \in { \in _0}\frac{{{\text{d}}{\phi _{\text{E}}}}}{{{\text{dt}}}} = \in { \in _0}{\text{A}}\frac{{{\text{dE}}}}{{{\text{dt}}}}$

$ = \in { \in _0} \times {\text{A}}{{\text{E}}_0}\omega \cos (\omega {\text{t}} - kx)$

${\rm{Jd}} = \in { \in _0}{{\rm{E}}_0}\omega $

$\frac{{{{\rm{J}}_{\rm{e}}}}}{{{{\rm{J}}_{\rm{d}}}}} = \frac{\sigma }{{ \in { \in _0}\omega }}$

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