A plane electromagnetic wave propagating alon | vedclass

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Question

(C) For a plane electromagnetic wave propagating in the direction of the wave vector $\vec{k}$,the electric field $\vec{E}$ and magnetic field $\vec{B

Vedclass · Accepted Answer

$E_{x}, B_{z}$ or $E_{z}, B_{x}$

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(C) For a plane electromagnetic wave propagating in the direction of the wave vector $\vec{k}$,the electric field $\vec{E}$ and magnetic field $\vec{B}$ are mutually perpendicular to each other and both are perpendicular to the direction of propagation $\vec{k}$.Given that the wave propagates along the y-direction,the direction of propagation is $\hat{j}$.Therefore,both $\vec{E}$ and $\vec{B}$ must lie in the xz-plane. This means their components can only be in the x or z directions.Specifically,if $\vec{E}$ is along the x-axis $(E_{x})$,then $\vec{B}$ must be along the z-axis $(B_{z})$ because $\vec{E} 	imes \vec{B}$ must be in the direction of propagation ($\hat{i} 	imes \hat{k} = -\hat{j}$,which is opposite to propagation,so we consider the cross product relation $\vec{E} 	imes \vec{B} \propto \vec{k}$).Checking the options: $\vec{E}$ and $\vec{B}$ must have components in the x and z directions. Option $(C)$ provides $E_{x}, B_{z}$ or $E_{z}, B_{x}$,which satisfy the condition that both fields are perpendicular to the y-direction of propagation.

$A$ plane electromagnetic wave propagating along the y-direction can have the following pair of electric field $(\vec{E})$ and magnetic field $(\vec{B})$ components.

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