For a plane electromagnetic wave, the electri | vedclass

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

Question

(B) Given, $\vec{E} = 90 \sin (0.5 	imes 10^{3} x + 1.5 	imes 10^{11} t) \hat{k} 	ext{ V/m}$.Comparing this with the standard wave equation $\vec{E

Vedclass · Accepted Answer

$\vec{B} = 3 	imes 10^{-7} \sin (0.5 	imes 10^{3} x + 1.5 	imes 10^{11} t) \hat{j} 	ext{ T}$

Vedclass · Answer

(B) Given, $\vec{E} = 90 \sin (0.5 	imes 10^{3} x + 1.5 	imes 10^{11} t) \hat{k} 	ext{ V/m}$.Comparing this with the standard wave equation $\vec{E} = E_{0} \sin (kx + \omega t) \hat{n}$, we get $E_{0} = 90 	ext{ V/m}$.The direction of propagation is along $-\hat{i}$ (since the argument is $kx + \omega t$).The amplitude of the magnetic field is $B_{0} = \frac{E_{0}}{c} = \frac{90}{3 	imes 10^{8}} = 3 	imes 10^{-7} 	ext{ T}$.The direction of propagation is given by the direction of $\vec{E} 	imes \vec{B}$.Here, $\vec{E}$ is along $\hat{k}$ and the direction of propagation is $-\hat{i}$.So, $\hat{k} 	imes \hat{B} = -\hat{i}$.Since $\hat{k} 	imes \hat{j} = \hat{i}$, it follows that $\hat{k} 	imes (-\hat{j}) = -\hat{i}$.Therefore, the magnetic field $\vec{B}$ must be along $\hat{j}$ (Wait, checking cross product: $\hat{k} 	imes \hat{j} = -\hat{i}$, so $\vec{B}$ is along $\hat{j}$).Thus, $\vec{B} = 3 	imes 10^{-7} \sin (0.5 	imes 10^{3} x + 1.5 	imes 10^{11} t) \hat{j} 	ext{ T}$.

For a plane electromagnetic wave, the electric field is given by $\overrightarrow{E} = 90 \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{k} \text{ V/m}$. The corresponding magnetic field $\vec{B}$ will be

Similar Questions

The frequency of an electromagnetic wave is $25 \ MHz$. If the magnitude of the electric field at a point at any instant is $6.3 \ V/m$,then the magnitude of the magnetic field at that point is ..... $Wb/m^2$.

$A$ plane electromagnetic wave of intensity $6 \, W/m^2$ strikes a small mirror of area $30 \, cm^2$,held perpendicular to the approaching wave. The momentum transmitted in $kg \cdot m/s$ by the wave to the mirror each second will be:

The sun delivers $10^{3} \,W m^{-2}$ of electromagnetic flux on the Earth's surface. The total power that is incident on a roof of dimensions $6 \,m \times 30 \,m$ is . . . . . . .

$A$ plane electromagnetic wave travels in free space along the $z$-axis. At a particular point in space, the electric field along the $x$-axis is $8.7 \ V \ m^{-1}$. The magnetic field along the $y$-axis is:

The electric field of a plane electromagnetic wave is given by $\overrightarrow{E} = E_{0}(\hat{x} + \hat{y}) \sin(kz - \omega t)$. Its magnetic field will be given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module