The electric field component of a monochromat | vedclass

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

Question

(C) Given,the electric field component of the monochromatic radiation is $\vec E = 2E_0 \hat i \cos kz \cos \omega t$.From Maxwell's equations,the rel

Vedclass · Accepted Answer

$\frac{2E_0}{c} \hat j \sin kz \sin \omega t$

Vedclass · Answer

(C) Given,the electric field component of the monochromatic radiation is $\vec E = 2E_0 \hat i \cos kz \cos \omega t$.From Maxwell's equations,the relationship between the electric field $\vec E$ and the magnetic field $\vec B$ is given by $
abla 	imes \vec E = -\frac{\partial \vec B}{\partial t}$.For a wave propagating in the $z$-direction with the electric field in the $x$-direction,the curl simplifies to $\frac{\partial E_x}{\partial z} = -\frac{\partial B_y}{\partial t}$.Calculating the partial derivative of $E_x$ with respect to $z$:$\frac{\partial E_x}{\partial z} = \frac{\partial}{\partial z} (2E_0 \cos kz \cos \omega t) = -2E_0 k \sin kz \cos \omega t$.Substituting this into the relation: $-2E_0 k \sin kz \cos \omega t = -\frac{\partial B_y}{\partial t}$.Therefore,$\frac{\partial B_y}{\partial t} = 2E_0 k \sin kz \cos \omega t$.Integrating with respect to $t$:$B_y = \int 2E_0 k \sin kz \cos \omega t \, dt = 2E_0 k \sin kz \left( \frac{\sin \omega t}{\omega} ight) = \frac{2E_0 k}{\omega} \sin kz \sin \omega t$.Since $c = \frac{\omega}{k}$,we have $\frac{k}{\omega} = \frac{1}{c}$.Thus,$B_y = \frac{2E_0}{c} \sin kz \sin \omega t$.Since the direction of propagation is along the $z$-axis and the electric field is along the $x$-axis,the magnetic field must be along the $y$-axis $(\hat j)$.Hence,$\vec B = \frac{2E_0}{c} \hat j \sin kz \sin \omega t$.

The electric field component of a monochromatic radiation is given by
$\vec E = 2E_0 \hat i \cos kz \cos \omega t$
Its magnetic field $\vec B$ is then given by

Similar Questions

The magnetic field of a plane electromagnetic wave is given by $\overrightarrow{ B } = 2 \times 10^{-8} \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{ j } \text{ T}$. The amplitude of the electric field would be:

For which of the following media will the wave propagation occur without experiencing attenuation?

Even though an electric field $E$ exerts a force $qE$ on a charged particle, the electric field of an $EM$ wave does not contribute to the radiation pressure (but transfers energy). Explain.

$A$ plane electromagnetic wave of wave intensity $6 \ W/m^2$ strikes a small mirror of area $40 \ cm^2$,held perpendicular to the approaching wave. The momentum transferred by the wave to the mirror each second will be:

$A$ plane electromagnetic wave of frequency $28 \, MHz$ travels in free space along the positive $x$-direction. At a particular point in space and time, the electric field is $9.3 \, V/m$ along the positive $y$-direction. The magnetic field (in $T$) at that point is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

The electric field component of a monochromatic radiation is given by$\vec E = 2E_0 \hat i \cos kz \cos \omega t$Its magnetic field $\vec B$ is then given by