Due to the presence of an em-wave whose elect | vedclass

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

Question

(B) The energy density of an electromagnetic wave is given by $u = \frac{1}{2} \epsilon_0 E^2$. The total energy $U$ contained in a cylinder of length

Vedclass · Accepted Answer

$200 \sin(\omega t - kx) \ NC^{-1}$

Vedclass · Answer

(B) The energy density of an electromagnetic wave is given by $u = \frac{1}{2} \epsilon_0 E^2$. The total energy $U$ contained in a cylinder of length $L$ and radius $R$ is $U = u 	imes V = \frac{1}{2} \epsilon_0 E^2 	imes (\pi R^2 L)$. Given that the energy $U$ remains the same for both cylinders,we have $U_1 = U_2$. $\frac{1}{2} \epsilon_0 E_1^2 \pi R_1^2 L_1 = \frac{1}{2} \epsilon_0 E_2^2 \pi R_2^2 L_2$. Since $L_1 = L_2$ and $R_2 = \frac{R_1}{2}$,the equation simplifies to $E_1^2 R_1^2 = E_2^2 (\frac{R_1}{2})^2$. $E_1^2 R_1^2 = E_2^2 \frac{R_1^2}{4}$. $E_2^2 = 4 E_1^2$,which implies $E_2 = 2 E_1$. Given $E_1 = 100 \ NC^{-1}$,we get $E_2 = 2 	imes 100 = 200 \ NC^{-1}$. Thus,the electric field is $200 \sin(\omega t - kx) \ NC^{-1}$.

Similar Questions

The oscillating magnetic field in a plane electromagnetic wave is given by $B_{y} = 5 \times 10^{-6} \sin(1000\pi(5x - 4 \times 10^{8}t)) \text{ T}$. The amplitude of the electric field will be:

The electric field of a plane electromagnetic wave propagating along the $x$-direction in vacuum is $\overrightarrow{E} = E_{0} \hat{j} \cos(\omega t - kx)$. The magnetic field $\overrightarrow{B}$ at the moment $t = 0$ is:

In a plane electromagnetic wave,the average value of ....... is zero.

An electromagnetic wave with angular frequency $\omega$ and wavelength $\lambda$ propagates in the $+y$ direction. Its magnetic field is directed along the $-x$ direction. The vector expression for the associated electric field (with amplitude $E_0$) is ...........

For an electromagnetic wave propagating through vacuum, $\vec{k}$, $\vec{E}$, and $\omega$ represent the propagation vector, electric field, and angular frequency, respectively. The magnetic field associated with this wave is represented by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module