Question

In an EM wave, $E=50 \sin (\omega t-k x)$. If $\mu=4 \mu_{0}$ and $\varepsilon=\varepsilon_{0}$, then average power per unit area (in $W / m ^{2}$ ) is

Answer 1

Intensity, $I=\frac{1}{2} \varepsilon v E_{0}^{2}$.
Now,
$v=\frac{1}{\sqrt{\mu \varepsilon}}=\frac{1}{\sqrt{\left(4 \mu_{0}\right)\left(\varepsilon_{0}\right)}}=\frac{c}{2} $
$I=\frac{1}{2} \varepsilon_{0}\left(\frac{c}{2}\right) E_{0}^{2}=\frac{1}{2} \times 8.8 \times 10^{-12} \times\left(\frac{3 \times 10^{8}}{2}\right)(50)^{2} $
$I=1.65 \,W / m ^{2}$