question_answer

The electric field of a plane polarized electromagnetic wave in free space at time  \[t=0\] is given by an expression \[\overrightarrow{E}\left( x,y \right)=10\widehat{j}\text{ }cos\left[ \left( 6x+8z \right) \right]\]. The magnetic field \[\overrightarrow{B}\left( x,\text{ }z,\text{ }t \right)\] is given by - (c is the velocity of light) [JEE Main 10-Jan-2019 Evening]

A) \[\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x+8z-10ct)]\]

B) \[\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z-10ct)]\]

C) \[\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x-8z+10ct)]\]

D) \[\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z+10ct)]\]

Correct Answer: B

Solution :

[b]

Phase angle of E at.

As E and B oscillate in same phase

Phase angle of B must be

Direction of wave propagation

Let  and unit vector in direction of propagation of EM wave is