Question

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 electromagnetic wave, whose electric field is $\overrightarrow{E}=30\hat{j}\sin (1.5\times {10}^{7}t-5\times {10}^{-2}x)\text{V/m}$. The maximum magnetic force experienced by the electron will be

(given $c=3\times {10}^8{\text{ms}}^{-1}$ & electron charge $=1.6\times {10}^{-19}\text{C})$

• A. $3.2\times {10}^{-18}\text{N}$
• B. $2.4\times {10}^{-18}\text{N}$
• C. $4.8\times {10}^{-19}\text{N}$
• D. $1.6\times {10}^{-19}\text{N}$

Answer 1

The correct option is C $4.8\times {10}^{-19}\text{N}$

In electromagnetic wave,
$\frac{E_0}{B_0}=c$
$\therefore$ Maximum value of magnetic field, $B_0=\frac{E_0}{c}$
Maximum magnetic force is
$F_{\text{max}}=qV{B}_{\text{max}}\sin 90°=\frac{q{V}_0{E}_0}{c}$
(Given $V_0=0.1\text{c}$ and $E_0=30\text{V/m}$)
$F_{\text{max}}=\frac{1.6\times {10}^{-19}\times 0.1\times 3\times {10}^8\times 30}{3\times {10}^8}=4.8\times {10}^{-19}\text{N}$