Question

The $rms$ value of the electric field of the light coming from the sun is $720N{C}^{-1}$. The average total energy density of the electromagnetic wave is

• A. $3.3\times 10^{-3}J{m}^{-3}$
• B. $4.85\times 10^{-6}J{m}^{-3}$
• C. $6.37\times 10^{-9}J{m}^{-3}$
• D. $81.35\times 10^{-12}J{m}^{-3}$

Answer 1

Answer: (B)

Total average energy density of electromagnetic wave is
$U_{av}=\frac{1}{2}{\epsilon }_0{E}_{rms}^2+\frac{1}{2{\mu }_0}{B}_{rms}^2$
$=\frac{1}{2}{\epsilon }_0{E}_{rms}^2+\frac{1}{2{\mu }_0}\left(\frac{E_{rms}^2}{c^2}\right)$
$\left(\because B_{rms}=\frac{E_{rms}}{c}\right)$
$=\frac{1}{2}{\epsilon }_0{E}_{rms}^2+\frac{1}{2{\mu }_0}{E}_{rms}^2{\epsilon }_0{\mu }_0$
$\left(\because c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}\right)$
$=\frac{1}{2}{\epsilon }_0{E}_{rms}^2+\frac{1}{2}{E}_{rms}^2={\epsilon }_0{E}_{rms}^2$
$=8.85\times 10^{-12}\times {\left(720\right)}^2$
$=4.58\times 10^{-6}J{m}^{-3}$