Problem — Amplitude E0 from intensity

Problem

An electromagnetic wave has average intensity $I=1{,}0\cdot 10^{-2}$ W/m². Calculate the amplitude $E_0$ of the electric field, knowing that $I=\tfrac12 c\varepsilon_0 E_0^2$.

Solution

Setup. We isolate $E_0$ from the intensity formula:

$E_0=\sqrt{\frac{2I}{c\,\varepsilon_0}}$

Calculation. With $I=1{,}0\cdot 10^{-2}$ W/m², $c=3{,}00\cdot 10^8$ m/s, $\varepsilon_0=8{,}85\cdot 10^{-12}$ F/m:

$E_0=\sqrt{\frac{2\cdot 1{,}0\cdot 10^{-2}}{3{,}00\cdot 10^8\cdot 8{,}85\cdot 10^{-12}}}\approx\sqrt{7{,}5}$

$\ev{E_0\approx 2{,}7\;\text{V/m}}$

Links

Topics: Onde elettromagnetiche Concepts: Intensità di un’onda