Question

The electric field in an electromagnetic wave is given by $E=\left(50N{C}^{-1}\right)\sin \omega (t-x/c)$
The energy contained in a cylinder of volume $V$ is $5.5\times 10^{-12}J$. The value of $V$ is ____ $c{m}^3$
$($ given ${ϵ}_0=8.8\times 10^{-12}{C}^2{N}^{-1}{m}^{-2})$

Answer 1

Answer: 500

$E=50\sin \left(\omega t-\frac{\omega }{c}\cdot x\right)$
Energy density $=\frac{1}{2}{\in }_0{E}_0^2$
Energy for volume $V=\frac{1}{2}{\in }_0{E}_0^2\cdot V=5.5\times 10^{-12}$
$\frac{1}{2}8.8\times 10^{-12}\times 2500V=5.5\times 10^{-12}$
$V=\frac{5.5\times 2}{2500\times 8.8}=.0005m^3$
$=.0005\times 10^6(c.m{)}^3$
$=500(c.m{)}^3$