Problem — Intensity from E0

Problem

A plane electromagnetic wave propagates in vacuum with electric field amplitude $E_0=100$ V/m. Calculate the average intensity carried, using $I=\tfrac12\varepsilon_0 c E_0^2$.

Solution

Formula. The average intensity (average power per unit area) of a plane EM wave is $I=\frac{1}{2}\varepsilon_0 c E_0^2$

Substituting the values. With $\varepsilon_0=8{,}85\cdot 10^{-12}$ F/m, $c=3{,}00\cdot 10^8$ m/s and $E_0=100$ V/m: $I=\frac{1}{2}\cdot 8{,}85\cdot 10^{-12}\cdot 3{,}00\cdot 10^8\cdot (100)^2$

Calculation. The square of the amplitude is $E_0^2=10^4$ V²/m²: $I=\frac{1}{2}\cdot 8{,}85\cdot 10^{-12}\cdot 3{,}00\cdot 10^8\cdot 10^4\approx 13{,}3\ \text{W/m}^2$

$\ev{I\approx 13{,}3\ \text{W/m}^2}$

Connections

Topics: Electromagnetic waves Concepts: Intensity of a wave