Question

In the vicinity of Earth's orbit around the Sun, the energy intensity of sunlight is about 1200 W/m2. What is the approximate magnitude of the electric field in the sunlight? (What you calculate is actually the "root-mean-square" or "rms" magnitude of the electric field, because in sunlight the magnitude of the electric field at a fixed location varies sinusoidally, and the intensity is proportional to E2.)

Answer 1

Answer:

672.29 W/m²

Explanation:

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

c = Speed of light = $3\times 10^8\ m/s$

I = Intensity of light = 1200 W/m²

$E_m$ = Maximum value electric field

Intensity of light is given by

$I=\frac{1}{2}\epsilon_0cE_m^2\\\Rightarrow E_m=\sqrt{\frac{2I}{\epsilon_0c}}\\\Rightarrow E_m=\sqrt{\frac{2\times 1200}{8.85\times 10^{-12}\times 3\times 10^8}}\\\Rightarrow E_m=950.765\ N/C$

RMS value

$E_r=\frac{E_m}{\sqrt2}\\\Rightarrow E_r=\frac{950.765}{\sqrt2}\\\Rightarrow E_r=672.29\ W/m^2$

The approximate magnitude of the electric field in the sunlight is 672.29 W/m²