Question

The magnetic field of a plane electromagnetic wave is given by:

$\vec{B} = B_0\hat{i}[cos(kz-wt)] + B_1\hat{j}cos(kz + wt)$

Where $B_0 = 2 \times 10^{-5}T$ and $B_1 = 1 \times 10^{-6}T$

The rms value of the force experienced by a stationary charge $Q = 10^{-3}C$ at $z = 0$ is $\frac{x}{\sqrt{2}}$.

Find the value of $x$.

Answer 1

6

Answer 2

The force on a stationary charge in an electromagnetic wave is solely due to the electric field. The peak magnetic field at $z=0$ is found by taking the magnitude of the vector sum of its components, which are in phase. This peak magnetic field is then used to calculate the peak electric field using the relation $E_{peak} = cB_{peak}$. The peak force is then $F_{peak} = QE_{peak}$. Finally, the RMS force is calculated as $F_{rms} = F_{peak}/\sqrt{2}$, and this is equated to the given form $\frac{x}{\sqrt{2}}$ to find $x$.