Problem — Amplitude and intensity summary

Problem

A plane electromagnetic wave in vacuum has electric field amplitude $E_0=100$ V/m. Calculate the amplitude of the magnetic field $B_0=E_0/c$ and the average intensity carried.

Solution

Amplitude of the magnetic field. In a plane EM wave the two fields are in phase and related by $E=cB$; for the amplitudes $B_0=\frac{E_0}{c}=\frac{100}{3{,}00\cdot 10^8}\approx 3{,}3\cdot 10^{-7}\ \text{T}$ that is, $B_0\approx 0{,}33\ \mu$T. The magnetic field is numerically tiny compared with the electric one, but it carries exactly the same energy density.

Average intensity. Using the electric amplitude: $I=\frac{1}{2}\varepsilon_0 c E_0^2=\frac{1}{2}\cdot 8{,}85\cdot 10^{-12}\cdot 3{,}00\cdot 10^8\cdot (100)^2\approx 13{,}3\ \text{W/m}^2$

$\ev{B_0\approx 3{,}3\cdot 10^{-7}\ \text{T}=0{,}33\ \mu\text{T},\qquad I\approx 13{,}3\ \text{W/m}^2}$

Connections

Topics: Electromagnetic waves Concepts: Intensity of a wave · Magnetic field