Problem — Ranking the intensity of four waves

Problem

Four plane electromagnetic waves in vacuum have electric field amplitude: (A) $E_0=10$ V/m; (B) $E_0=100$ V/m; (C) $E_0=300$ V/m; (D) $E_0=50$ V/m. Order their intensities (time average of the Poynting vector) from smallest to largest. Remember that $I=\tfrac12\varepsilon_0 c E_0^2$.

Solution

Setup. In the formula $I=\tfrac12\varepsilon_0 c E_0^2$ the factors $\tfrac12\varepsilon_0 c$ are the same for all the waves: the intensity depends only on $E_0^2$.

$I\propto E_0^2$

Step — compare the squares of the amplitudes.

$10^2=100<50^2=2500<100^2=10^4<300^2=9\cdot 10^4$

Since the intensity grows with $E_0^2$, the order of the intensities follows the same order.

$\ev{I_A<I_D<I_B<I_C}$

Links

Topics: Onde elettromagnetiche Concepts: Intensità di un’onda Skills: Ragionamento di ranking