# An electron is constrained to move along the y-axis with a speed of $0.1\; c$ ($c$ is the speed of light) in the presence of electromagnetic wave, whose electric field is $\vec{E}=30\; \hat{j}\sin (1.5\times 10^{7}t-5\times 10^{-2}x)V/m.$ The maximum magnetic force experienced by the electron will be : (given $c=3\times 10^{8}ms^{-1}$ and electron charge $=1.6\times 10^{-19}C$ ) Option: 1   Option: 2 Option: 3 Option: 4

$\begin{array}{l} \Rightarrow \mathrm{E}=\overrightarrow{\mathrm{E}}=30 \hat{\mathrm{j}} \sin \left(1.5 \times 10^{7} \mathrm{t}-5 \times 10^{-2} \mathrm{x}\right) \mathrm{V} / \mathrm{m} \\ \Rightarrow \mathrm{B} \Rightarrow \mathrm{E} / \mathrm{V} \Rightarrow \frac{30}{1.5 \times 10^{7}} \times 5 \times 10^{-2} \\ \Rightarrow 10^{-7} \text {Tesla } \\ \Rightarrow \mathrm{F}_{\mathrm{mag}}=\mathrm{q}(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})=|\mathrm{qVB}| \\ =1.6 \times 10^{-19} \times 0.1 \times 3 \times 10^{8} \times 10^{-7} \\ =4.8 \times 10^{-19} \mathrm{~N} \end{array}$

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