Q. A cube of edge a has its edges parallel to $x,\ y$ and $z$-axis of rectangular coordinate system. A uniform electric field $\overrightarrow{E}$ is parallel to $y$-axis and a uniform magnetic field is $\overrightarrow{E}$ parallel to $x$-axis. The rate at which flows through each face of the cube is
A) $\frac{a^{2}.EB}{2\mu_{0}}$ parallel to $x - y$ plane and zero in others
B) $\frac{a^{2}EB}{\mu_{0}}$ parallel to $x - y$ plane and zero in others
C) $\frac{a^{2}EB}{2\mu_{0}}$ from all faces
D) $\frac{a^{2}EB}{2\mu_{0}}$ parallel; to $y - \mathcal{z}$ faces and zero in others
Explanation
(b) Energy flowing per sec per unit area from a face is $= \frac{1}{\mu_{0}}\lbrack\overrightarrow{\mathbf{E}}\mathbf{\times}\overrightarrow{\mathbf{B}}\rbrack$. It will be in the negative $\mathcal{z}$-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 a face in $x - y$ plane$= \frac{1}{\mu_{0}}\left( EB\sin{90{^\circ}} \right)a^{2} = \frac{EBa^{2}}{\mu_{0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.