Question

During the propagation of an electromagnetic wave in a medium -

• A. both electric and magnetic energy densities are zero.
• B. electric energy density is double of the magnetic energy density.
• C. electric energy density is half of the magnetic energy density.
• D. electric energy density is equal to the magnetic energy density.

Answer 1

The correct option is D electric energy density is equal to the magnetic energy density.

We know that electric energy density is given by,

$u_E=\frac{1}{2}{ϵ}_0{E}_0^2$

Also, magnetic energy density is given by,

$u_B=\frac{B_0^2}{2{\mu }_0}$

Further,

$B_0=\frac{E_0}{c}$, and

$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$

So,

$u_B={\left(\frac{E_0}{c}\right)}^2\times \frac{1}{2{\mu }_0}$

$\Rightarrow u_B=\frac{E_0^2}{2{\mu }_0}\times {\mu }_0{ϵ}_0$

$\Rightarrow u_B=\frac{1}{2}{ϵ}_0{E}_0^2=u_E$

Therefore, we can say that in propagation of an electromagnetic wave, energy is equally divided between the electric and the magnetic fields.

Hence, option $\left(D\right)$ is the correct answer.