Question

A cube of edge $a$ has its edges parallel to $x,y$ and $z-$axis of rectangular coordinate system. A uniform electric field $E$ parallel to $y-$axis and a uniform magnetic field is parallel to $x-$axis. The rate at which energy flows through each face of the cube is:

• A. zero in all faces
• B. $\frac{a^{2}EB}{2{\mu }_0}$ parallel to $xy$ plane face and zero in others
• C. $\frac{a^{2}EB}{{\mu }_0}$ parallel to $xy$ plane face and zero in others
• D. $\frac{a^{2}EB}{2{\mu }_0}$ all faces

Answer 1

The correct option is C $\frac{a^{2}EB}{{\mu }_0}$ parallel to $xy$ plane face and zero in others

Poynting Vector or Energy Flow per unit area in an Electromagnetic Field is given by:
$\overrightarrow{S}=\frac{1}{{\mu }_o}\overrightarrow{E}\times \overrightarrow{B}$
Now as $\overrightarrow{E}\&\overrightarrow{B}$ are perpendicular
So $S=\frac{1}{{\mu }_o}EB\left(directionzaxis\right)$
Now total energy flow: $=S\times Area=\frac{1}{{\mu }_o}EB{a}^2$ along faces parallel to x-y plane as wave direction is perpendicular to the remaining faces..

For other faces, energy flow through them is zero as wave direction is parallel to the remaining faces.