An electromagnetic wave travels along the z-a | vedclass

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(A) An electromagnetic wave travels in the direction of the Poynting vector $\vec{S} = \frac{1}{\mu_0} (\vec{E} 	imes \vec{B})$.Given that the wave t

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$E_x, B_y$

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(A) An electromagnetic wave travels in the direction of the Poynting vector $\vec{S} = \frac{1}{\mu_0} (\vec{E} 	imes \vec{B})$.Given that the wave travels along the $z$-axis,the direction of propagation is $\hat{k}$.We know that $\vec{E} 	imes \vec{B}$ must be in the direction of $\hat{k}$.For option $A$,$\vec{E} = E_x \hat{i}$ and $\vec{B} = B_y \hat{j}$.Calculating the cross product: $\hat{i} 	imes \hat{j} = \hat{k}$.Thus,$E_x \hat{i} 	imes B_y \hat{j} = (E_x B_y) \hat{k}$,which is along the $z$-axis.Therefore,the pair $(E_x, B_y)$ generates an electromagnetic wave traveling along the $z$-axis.

An electromagnetic wave travels along the $z$-axis. Which of the following pairs of space and time-varying fields would generate such a wave?

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