The electric field for a plane electromagneti | vedclass

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(A) For an electromagnetic wave,the direction of propagation is given by the direction of the vector $\vec E 	imes \vec B$.Given that the wave travel

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in the $+x$ direction and in phase with the electric field $\vec E$

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(A) For an electromagnetic wave,the direction of propagation is given by the direction of the vector $\vec E 	imes \vec B$.Given that the wave travels in the $+y$ direction,we have the direction of propagation $\hat{v} = \hat{j}$.The electric field $\vec E$ is in the $+z$ direction,so $\vec E = E_0 \hat{k}$.Using the relation $\vec E 	imes \vec B = 	ext{direction of propagation}$,we have $\hat{k} 	imes \vec B = \hat{j}$.We know that $\hat{k} 	imes \hat{i} = \hat{j}$. Therefore,$\vec B$ must be in the $+x$ direction.Also,in an electromagnetic wave,the electric and magnetic fields are always in phase.Thus,the magnetic field $\vec B$ is in the $+x$ direction and in phase with the electric field $\vec E$.

The electric field for a plane electromagnetic wave travelling in the $+y$ direction is shown in the figure. Consider a point where the electric field is in the $+z$ direction. The magnetic field $\vec B$ is

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