Which of the following pairs of components ca | vedclass

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(B) In a plane electromagnetic wave,the electric field vector $\vec{E}$,the magnetic field vector $\vec{B}$,and the direction of propagation $\vec{k}$

Vedclass · Accepted Answer

$E_y, B_z$

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(B) In a plane electromagnetic wave,the electric field vector $\vec{E}$,the magnetic field vector $\vec{B}$,and the direction of propagation $\vec{k}$ are mutually perpendicular to each other.Specifically,the direction of propagation is given by the direction of the Poynting vector $\vec{S} = \frac{1}{\mu_0} (\vec{E} 	imes \vec{B})$.For a plane wave propagating along a specific axis (e.g.,$x$-axis),the electric field must be in the $y$-direction $(E_y)$ and the magnetic field must be in the $z$-direction $(B_z)$,or vice versa.If the wave propagates along the $x$-axis,then $\vec{E} = E_y\hat{j}$ and $\vec{B} = B_z\hat{k}$.Thus,the pair $(E_y, B_z)$ is a valid combination for an electromagnetic wave propagating along the $x$-axis.

Which of the following pairs of components can produce a plane electromagnetic wave propagating in a direction such that the electric field $\vec{E} = (E_x\hat{i} + E_y\hat{j} + E_z\hat{k})$ and magnetic field $\vec{B} = (B_x\hat{i} + B_y\hat{j} + B_z\hat{k})$ vary with position and time?

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