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Question

(A) The direction of energy propagation of an electromagnetic wave is given by the direction of the Poynting vector,$\overrightarrow{S} = \overrightar

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Positive direction of $x$

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(A) The direction of energy propagation of an electromagnetic wave is given by the direction of the Poynting vector,$\overrightarrow{S} = \overrightarrow{E} 	imes \overrightarrow{B}$.Given that the energy transport is in the negative $z$ direction,the direction of the Poynting vector is $-\hat{k}$.The direction of the electric field $\overrightarrow{E}$ is given as the positive $y$ direction,which is $+\hat{j}$.We know that $\overrightarrow{S} \propto \overrightarrow{E} 	imes \overrightarrow{B}$.Substituting the known directions: $(-\hat{k}) = (+\hat{j}) 	imes \overrightarrow{B}$.Using the properties of cross products of unit vectors: $\hat{j} 	imes \hat{i} = -\hat{k}$.Therefore,the direction of the magnetic field $\overrightarrow{B}$ must be the positive $x$ direction $(+\hat{i})$.

All electromagnetic waves transport energy in the negative $z$ direction. At a certain point and time,the direction of the electric field of the wave is along the positive $y$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

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