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

Answer 1

The correct option is A

$4.58\times {10}^{-6}J{m}^{-3}$

Step 1: Given Data

the RMS value of the electric field $E_{rms}=720N{C}^{-1}$

Step 2: Formula Used

The total average energy $E_{avg}={\mathrm{\epsilon }}_{\mathrm{o}}{\mathrm{E}}_{\mathrm{rms}}^2$

${\mathrm{E}}_{rms}$is the RMS value of the electric field of the light coming from the sun.

where ${\epsilon }_0$ is the permittivity of free space.

Step 3: Calculating the total average energy

Total average energy,

$$\begin{gathered} E_{avg}={\mathrm{\epsilon }}_{\mathrm{o}}{\mathrm{E}}_{\mathrm{rms}}^2 \\ {E}_{avg}=8.854\times {10}^{-12}\times \left(720\right){\mathrm{Jm}}^{-3} \\ {E}_{avg}=4.58\times {10}^{-6}{\mathrm{Jm}}^{-3} \end{gathered}$$

Therefore, the average total energy density of the electromagnetic wave is $4.58\times {10}^{-6}{\mathrm{Jm}}^{-3}$, and the correct answer is option (A).