Answer to Question #101161 in Electricity and Magnetism for M S

Question

the earth receives about 1300 watt/m2 radiant energy from the sun. Assuming the energy to be in the form of plane polarised monochromatic waves and assuming normal incidence calculate the magnitude of electric field vector in the sun light.

Answer 1

So, we have that

$I=\langle S \rangle=1300 watt/m^2$

$S=EH$

where

$E=E_0\cos(\omega t-kx)$

and

$H=H_0\cos(\omega t-kx)$

$S=E_0H_0\cos^2(\omega t-kx)$

$\langle S\rangle=\frac{1}{2}E_0H_0$

$E_0\sqrt{\epsilon \epsilon_0}=H_0\sqrt{\mu \mu_0}\to H_0=\sqrt{\frac{\epsilon_0}{\mu_0}}E_0$

Finally

$I=\frac{1}{2}E_0\sqrt{\frac{\epsilon_0}{\mu_0}}E_0=\frac{1}{2}E_0^2\sqrt{\frac{\epsilon_0}{\mu_0}}\to E_0=\sqrt{2I\sqrt{\frac{\mu_0}{\epsilon_0}}}$

So,

$E_0=\sqrt{2I\sqrt{\frac{\mu_0}{\epsilon_0}}}=\sqrt{2\cdot 1300\sqrt{\frac{4\cdot 3.14\cdot 10^{-7}}{8.85\cdot 10^{-12}}}}=990 \frac{V}{m}$

The End!