An electron is constrained to move along the $y$-axis with a speed of $0.1c$ ($c$ is the speed of light) in the presence of an electromagnetic wave, whose electric field is $\vec E = 30\hat j\sin(1.5\times10^{7}t - 5\times10^{-2}x)\ \text{V m}^{-1}$, where $t$ is in seconds and $x$ is in metres. The maximum magnetic force experienced by the electron will be: (given $c = 3\times10^{8}\ \text{m s}^{-1}$ and electron charge $= 1.6\times10^{-19}$ C)
Answer: (C) $4.8\times10^{-19}\ \text{N}$
$B_0 = \dfrac{E_0}{c} = \dfrac{30}{3\times10^{8}} = 10^{-7}$ T, directed along $z$ (wave along $x$, $\vec E$ along $y$), so it is perpendicular to the electron's velocity.
$$F_{max} = evB_0 = 1.6\times10^{-19}\times3\times10^{7}\times10^{-7} = 4.8\times10^{-19}\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics