The electric fields of two plane electromagnetic plane waves in vacuum are given by
$\overrightarrow {{E_1}} = {E_0}\widehat j\cos \left( {\omega t - kx} \right)$ and
$\overrightarrow {{E_2}} = {E_0}\widehat k\cos \left( {\omega t - ky} \right)$
At t = 0, a particle of charge q is at origin with
a velocity $\overrightarrow v = 0.8c\widehat j$ (c is the speed of light in vacuum). The instantaneous force experienced by the particle is :

$\overrightarrow {{E_1}} = {E_0}\widehat j\cos \left( {\omega t - kx} \right)$ <br><br>Its corresponding magnetic field will be <br><br>$$\overrightarrow {{B_1}} = {{{E_0}} \over c}\widehat k\cos \left( {\omega t - kx} \right)$$ <br><br>$\overrightarrow {{E_2}} = {E_0}\widehat k\cos \left( {\omega t - ky} \right)$ <br><br>Also its corresponding magnetic field will be <br><br>$$\overrightarrow {{B_2}} = {{{E_0}} \over c}\widehat i\cos \left( {\omega t - ky} \right)$$ <br><br>Net force on charge particle <br><br>= $$q\overrightarrow {{E_1}} + q\overrightarrow {{E_2}} + q\overrightarrow v \times \overrightarrow {{B_1}} $$$+ q\overrightarrow v \times \overrightarrow {{B_2}}$ <br><br>= ${q{E_0}\widehat j}$ + ${q{E_0}\widehat k}$ + $$q\left( {0.8c\widehat j} \right) \times \left( {{{{E_0}} \over c}\widehat i} \right)$$ + $$q\left( {0.8c\widehat j} \right) \times \left( {{{{E_0}} \over c}\widehat i} \right)$$ <br><br>= ${E_0}q\left( {0.8\widehat i + \widehat j + 0.2\widehat k} \right)$