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The magnetic field of a plane electromagnetic wave is given by
$\vec B\, = {B_0}\hat i\,[\cos \,(kz - \omega t)]\, + \,{B_1}\hat j\,\cos \,(kz - \omega t)$ where ${B_0} = 3 \times {10^{-5}}\,T$ and ${B_1} = 2 \times {10^{-6}}\,T$. The rms value of the force experienced by a stationary charge $Q = 10^{-4} \,C$ at $z = 0$ is closet to
$0.9\,N$
$3\times 10^{-2}\,N$
$0.1\,N$
$0.6\,N$
Solution
Maximum electric field $E=(B)(C)$
$\overrightarrow{\mathrm{E}}_{0}=\left(3 \times 10^{-5}\right) \mathrm{c}(-\hat{\mathrm{j}})$
$\overrightarrow{\mathrm{E}}_{1}=\left(2 \times 10^{-6}\right) \mathrm{c}(-\hat{\mathrm{i}})$
Maximum force
$\overrightarrow{\mathrm{F}}_{\mathrm{net}}=10^{-4} \times 3 \times 10^{8} \sqrt{\left(3 \times 10^{-5}\right)^{2}+\left(2 \times 10^{-6}\right)^{2}}=0.9\, \mathrm{N}$
$\mathrm{F}_{\mathrm{ms}}=\frac{\mathrm{F}_{0}}{\sqrt{2}}=0.6\, \mathrm{N}$ (approx)
