# An electron is constrained to move along

Question:

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 $\vec{E}=30 \hat{j}$ $\sin \left(1.5 \times 10^{7} t-5 \times 10^{-2} x\right) \mathrm{V} / \mathrm{m}$. The maximum magnetic force experienced by the electron will be :

(given $c=3 \times 10^{8} \mathrm{~ms}^{-1} \&$ electron charge $\left.=1.6 \times 10^{-19} \mathrm{C}\right)$

1. (1) $3.2 \times 10^{-18} \mathrm{~N}$

2. (2) $2.4 \times 10^{-18} \mathrm{~N}$

3. (3) $4.8 \times 10^{-19} \mathrm{~N}$

4. (4) $1.6 \times 10^{-19} \mathrm{~N}$

Correct Option: , 3

Solution:

(3) In electromagnetic wave, $\frac{E_{0}}{B_{0}}=C$

$\therefore$ Maximum value of magnetic field, $B_{0}=\frac{E_{0}}{C}$

$F_{\max }=q V B_{\max } \sin 90^{\circ}=\frac{q V_{0} E_{0}}{C}$

(Given $V_{0}=0.1 \mathrm{C}$ and $E_{0}=30$ )

$=\frac{1.6 \times 10^{-19} \times 0.1 \times 3 \times 10^{8} \times 30}{3 \times 10^{8}}=4.8 \times 10^{-19} \mathrm{~N}$