Question

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is $E=6V{{m}^{-1}}$ along y-direction. Its corresponding magnetic field component, $B$ would be
$A.6\times {{10}^{-8}}T$along z-direction.
$B.6\times {{10}^{-8}}T$along x-direction.
$C.2\times {{10}^{-8}}T$along z-direction.
$D.2\times {{10}^{-8}}T$along y-direction.

Answer 1

Concept of propagation of electromagnetic waves will be used in the problem to solve it correctly. The waves which are created as a result of vibrations between an electric field and a magnetic field are called electromagnetic waves. During the propagation of the electromagnetic wave, electric field and magnetic field are mutually perpendicular to each other.
Formula Used:
To solve this problem, we will apply the following relation:-
$E=cB$

Complete answer:
Electromagnetic waves are the waves which are created as a result of vibrations between electric and magnetic fields. We will use the following relation to find the required value of the magnetic field, $B$.
$E=cB$ Where, $c$ is speed of light in free space, $E$is electric field and $B$ is magnetic field.
$B=\dfrac{E}{c}$
$B=\dfrac{6}{3\times {{10}^{8}}}$As value of ($c=3\times {{10}^{8}}m/s$in free space)
$B=\dfrac{6\times {{10}^{-8}}}{3}$
$B=2\times {{10}^{-8}}T$
The direction of propagation of electromagnetic waves is in x-direction, electric field is in y-direction. As the electric field, magnetic field and direction of propagation of electromagnetic waves are mutually perpendicular to each other. Therefore, the magnetic field will travel in z-direction.
Hence, Magnetic field, $B=2\times {{10}^{-8}}m/s$ in z-direction.

So, option $(C)$ is correct among the options given above.

Additional Information:
An accelerated charge produces electromagnetic waves. The frequency of the oscillating wave is the same as that of accelerated charge. The velocity of an electromagnetic wave does not depend on the amplitude of the field vector. The electric field and magnetic field both oscillate in the same phase. The electromagnetic wave travels through vacuum with the speed of light.

Note:
Electromagnetic waves propagate with the velocity of light in free space. This fact is very important in analysing the propagation of the electromagnetic wave. It should also be noted that the electromagnetic wave, electric field and magnetic field are mutually perpendicular to each other.