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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 $\overrightarrow{ E }=30 \hat{ j } \sin \left(1.5 \times 10^{7} t -5 \times 10^{-2} x \right)\, V / m$ The maximum magnetic force experienced by the electron will be: (given $c=3 \times 10^{8}\, ms ^{-1}$ and electron charge $\left.=1.6 \times 10^{-19} C \right)$
$1.6 \times 10^{-19} N$
$4.8 \times 10^{-19} N$
$3.2 \times 10^{-18} N$
$2.4 \times 10^{-18} N$
Solution
$\Rightarrow E =\overrightarrow{ E }=30 \hat{ j } \sin \left(1.5 \times 10^{7} t -5 \times 10^{-2} x \right) V / m$
$\Rightarrow B \Rightarrow E / V \Rightarrow \frac{30}{1.5 \times 10^{7}} \times 5 \times 10^{-2}$
$\Rightarrow 10^{-7}$ Tesla
$\Rightarrow F _{ mag }= q (\overrightarrow{ V } \times \overrightarrow{ B })=| q VB |$
$=1.6 \times 10^{-19} \times 0.1 \times 3 \times 10^{8} \times 10^{-7}$
$=4.8 \times 10^{-19} N$
