Question

The electric field in an electromagnetic wave is given by $E=\left(50N{C}^{-1}\right)\sin \omega (t-\frac{x}{c})$.
Find the electrical energy contained in a cylinder of cross-section 10 $c{m}^2$ and length 50 $cm$ along the x-axis.

• A. $5.5\times {10}^{-12}J$
• B. $1.1\times {10}^{-8}J$
• C. $5\times {10}^{-4}J$
• D. $1.1\times {10}^{-12}J$

Answer 1

The correct option is A $5.5\times {10}^{-12}J$

Given that
$E=\left(50N{C}^{-1}\right)\sin \omega (t-\frac{x}{c})$
$E_0=50{\text{NC}}^{-1}A=10{\text{cm}}^{2}L=50\text{cm}$
Now we know energy density is given by
$U_D=\frac{1}{2}{\epsilon }_0{E}_0^2$
$\Rightarrow U_D=\frac{1}{2}\times 8.85\times {10}^{-12}\times {50}^2$
$\Rightarrow U_D=1.1\times {10}^{-8}{\text{J/m}}^3$
So energy contained can be obtained by
$U_T=U_D\times V$
where $V$ is the volume
$\Rightarrow U_T=U_D\times A\times L$
$\Rightarrow U_T=1.1\times {10}^{-8}\times 50\times 10\times {10}^{-4}$
$\Rightarrow U_T=5.5\times {10}^{-12}\text{J}$