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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.)

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Answer:

672.29 W/m²

Explanation:

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

c = Speed of light = [tex]3\times 10^8\ m/s[/tex]

I = Intensity of light = 1200 W/m²

[tex]E_m[/tex] = Maximum value electric field

Intensity of light is given by

[tex]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[/tex]

RMS value

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

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

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