A cube of edge ‘a’ has its edges parallel to X,Y and Z-axes of rectangular coordinate system. In an electromagnetic wave, uniform electric field $\vec{E}$ is parallel to Y-axis and a uniform magnetic field is $\vec{B}$ parallel to X-axis. The rate at which energy flows through each face of the cube is

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$\frac{a^{2} E B}{2 μ_{0}}$ parallel to X – Y plane and zero in other

$\frac{a^{2} E B}{μ_{0}}$ parallel to X-Y plane and zero in others

$\frac{a^{2} E B}{2 μ_{0}}$ from all faces

$\frac{a^{2} E B}{2 μ_{0}}$ parallel to Y-Z faces and zero in others

answer is B.

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Detailed Solution

Energy flowing per sec per unit area from a face is $= \frac{1}{μ_{0}} (\vec{E} \times \vec{B})$ it will be in the negative z-direction. It shows that the energy will be flowing infaces parallel to x-y plane and is zero in all other faces. Total energy flowing per second from face in x-y plane $= \frac{1}{μ_{0}} (E B \sin 90^{0}) a^{2} = \frac{E B a^{2}}{μ_{0}}$