Question

In a plane electromagnetic wave the electric field varies with the time having an amplitude of $1.0V{m}^{-1}$. Find the average energy density of magnetic field and that of electric field.

Answer 1

Average energy density of both electric and magnetic field will be same.

Now total average energy density = $\frac{1}{2{\mu }_0}{B}^2$

or, $B=\frac{E}{C}=\left(\frac{1}{3\times {10}^8}\right)T$

$\therefore$ Energy density =$\frac{1}{2\times 4\pi \times {10}^{-7}}\times (\frac{1}{3\times {10}^8}{)}^2$

$=44\times {10}^{-12}J{m}^{-3}$

This would be equally distributed in magnetic and electric field.

Hence average energy density of magnetic field = Average energy density of electric field

$=2.2\times {10}^{-12}J{m}^{-3}$(each)