Question

A beam of light travelling along $X$-axis is described by the electric field $E_Y=600\frac{V}{m}\cdot \sin \omega (t-\frac{x}{c})$, the maximum magnetic force on a charge $q=2e$, moving along $Y$-axis with the speed of $3\times {10}^{8}m/s$ is

• A. $19.2\times {10}^{-17}N$
• B. $1.92\times {10}^{-17}N$
• C. $0.192N$
• D. None of these

Answer 1

The correct option is A $19.2\times {10}^{-17}N$

Given, electric field, $E_Y=600\frac{V}{m}.\sin \omega (t-\frac{x}{c})$ ....(i)
We know that,
$E=E_0\sin \omega (t-\frac{x}{c})$ .....(ii)
On comparing equations (i) and (ii), we get
$E_0=600V/m$ and $C=3\times {10}^{8}m/s$
Maximum magnetic field,
$B_0=\frac{E_0}{C}$
$B_0=\frac{600}{3\times {10}^8}=2\times {10}^{-6}T$
$\therefore F_m=qv{B}_0=2ev{B}_0$
$=2\times 1.6\times {10}^{-19}\times 3\times {10}^8\times 2\times {10}^{-6}$
$=19.2\times {10}^{-17}N$