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(B) The direction of propagation of an electromagnetic wave is given by the direction of the Poynting vector,which is $\vec{E} 	imes \vec{B}$.Given t

Vedclass · Accepted Answer

$-\hat{j} + \hat{k}, -\hat{j} - \hat{k}$

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(B) The direction of propagation of an electromagnetic wave is given by the direction of the Poynting vector,which is $\vec{E} 	imes \vec{B}$.Given the wave propagates in the $x$-direction,we must have $\vec{E} 	imes \vec{B} \parallel \hat{i}$.For option $B$: $\vec{E} = -\hat{j} + \hat{k}$ and $\vec{B} = -\hat{j} - \hat{k}$.Calculating the cross product: $\vec{E} 	imes \vec{B} = (-\hat{j} + \hat{k}) 	imes (-\hat{j} - \hat{k}) = (-\hat{j} 	imes -\hat{j}) + (-\hat{j} 	imes -\hat{k}) + (\hat{k} 	imes -\hat{j}) + (\hat{k} 	imes -\hat{k}) = 0 + \hat{i} + \hat{i} + 0 = 2\hat{i}$.Since $2\hat{i}$ is in the $x$-direction,option $B$ is correct.

For a plane electromagnetic wave propagating in the $x$-direction,which one of the following combinations gives the correct possible directions for the electric field $(\vec{E})$ and magnetic field $(\vec{B})$ respectively?

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