A plane electromagnetic wave of angular frequ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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 $\frac{J_c}{J_d} = \frac{\sigma E_0}{\varepsilon \varepsilon_0 E_0 \omega} = \frac{\sigma}{\varepsilon \varepsilon_0 \omega}$.

List-$I$	List-$II$
$A$. Gauss's Law in Electrostatics	$I$. $\oint \vec{E} \cdot d \vec{l} = -\frac{d \phi_B}{d t}$
$B$. Faraday's Law	$II$. $\oint \vec{B} \cdot d \vec{A} = 0$
$C$. Gauss's Law in Magnetism	$III$. $\oint \vec{B} \cdot d \vec{l} = \mu_0 i_C + \mu_0 \epsilon_0 \frac{d \phi_E}{d t}$
$D$. Ampere-Maxwell Law	$IV$. $\oint \vec{E} \cdot d \vec{s} = \frac{q}{\epsilon_0}$

$A$ 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.

Similar Questions

What contradiction is found by using Ampere's circuital law to obtain the magnetic field during the charging of a capacitor?

What was the primary difficulty in establishing the wave theory of light,and who explained it?

Write Maxwell's equations.

Vedclass Test Series

Exam Paper Generator

Online Exam Module