Question

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

• A. $3.3\times {10}^{-3}J{m}^{-3}$
• B. $4.58\times {10}^{-6}J{m}^{-3}$
• C. $6.37\times {10}^{-9}J{m}^{-3}$
• D. $81.35\times {10}^{-12}J{m}^{-3}$

Answer 1

The correct option is B $4.58\times {10}^{-6}J{m}^{-3}$

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