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Question

(B) For an electromagnetic wave,the electric field $\vec{E}$ and magnetic field $\vec{B}$ are mutually perpendicular,i.e.,$\vec{E} \cdot \vec{B} = 0$.

Vedclass · Accepted Answer

$(-2\hat{i} - 3\hat{j})$ and $(3\hat{i} - 2\hat{j})$

Vedclass · Answer

(B) For an electromagnetic wave,the electric field $\vec{E}$ and magnetic field $\vec{B}$ are mutually perpendicular,i.e.,$\vec{E} \cdot \vec{B} = 0$.Also,the direction of propagation is given by the direction of $\vec{E} 	imes \vec{B}$,which must be along the $z$-direction (i.e.,$\hat{k}$).Checking option $(b)$:$\vec{E} \cdot \vec{B} = (-2\hat{i} - 3\hat{j}) \cdot (3\hat{i} - 2\hat{j}) = (-2)(3) + (-3)(-2) = -6 + 6 = 0$.$\vec{E} 	imes \vec{B} = (-2\hat{i} - 3\hat{j}) 	imes (3\hat{i} - 2\hat{j}) = 4(\hat{i} 	imes \hat{j}) - 9(\hat{j} 	imes \hat{i}) = 4\hat{k} - 9(-\hat{k}) = 4\hat{k} + 9\hat{k} = 13\hat{k}$.Since the result is in the $z$-direction,option $(b)$ is correct.

For plane electromagnetic waves propagating in the $z$-direction,which one of the following combinations gives the correct possible direction for $\vec{E}$ and $\vec{B}$ fields respectively?

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