Problem — Amplitude E0 from solar irradiance

Problem

A plane electromagnetic wave has average intensity $\langle I\rangle = 1{,}4\;\text{kW/m}^2$ (the solar irradiance in Earth orbit). Calculate the amplitude $E_0$ of the electric field, using the relation $\langle I\rangle = E_0^2/(2c\mu_0)$.

Solution

Setup. We invert the average intensity formula to find $E_0$:

$E_0 = \sqrt{2c\mu_0\,\langle I\rangle}$

Numerical substitution. With $c = 3{,}00\cdot 10^8\;\text{m/s}$, $\mu_0 = 4\pi\cdot 10^{-7}\;\text{F/m}$ and $\langle I\rangle = 1{,}4\cdot 10^3\;\text{W/m}^2$:

$E_0 = \sqrt{2\cdot 3{,}00\cdot 10^8\cdot 4\pi\cdot 10^{-7}\cdot 1{,}4\cdot 10^3} \approx 1{,}0\cdot 10^3\;\text{V/m}$

$\ev{E_0 \approx 1{,}0\cdot 10^3\;\text{V/m}}$

About a kilovolt per metre: the typical amplitude of the electric field of sunlight just outside the atmosphere.

Collegamenti

Argomenti: Onde elettromagnetiche Concetti: Intensità di un’onda