Question

A plane electromagnetic wave propagating in the $x-$direction in vacuum has wavelength of $6.0\text{mm}$. The electric field is in the $y-$direction and its maximum magnitude is $33{\text{Vm}}^{-1}$.

$\left(iii\right)$ Find the average energy density of the electromagnetic wave.

​​​​​​​$[$1 Mark$]$

• A. $4.82\times {10}^{-12}{\text{Jm}}^{-3}$
• B. $4.82\times {10}^{-9}{\text{Jm}}^{-3}$
• C. $9.58\times {10}^{-12}{\text{Jm}}^{-3}$
• D. $1.23\times {10}^{-12}{\text{Jm}}^{-3}$

Answer 1

The correct option is B $4.82\times {10}^{-9}{\text{Jm}}^{-3}$

The average energy density of electromagnetic wave is given by
$U_{av}=\frac{1}{2}{\epsilon }_0{E}_0^2$

$U_{av}=\frac{1}{2}\times 8.854\times {10}^{-12}\times (33{)}^2$

$U_{av}=4.82\times {10}^{-9}{\text{Jm}}^{-3}$