Question

A stationary particle of charge q = 2.4 × 10^-8 C is placed in a laser beam (an electromagnetic wave) whose intensity is 2.7 × 10^3 W/m^2. Determine the maximum magnitude of the (a) electric and (b) magnetic forces exerted on the charge. If the charge is moving at a speed of 3.7 × 104 m/s perpendicular to the magnetic field of the electromagnetic wave, find the maximum magnitudes of the (c) electric and (d) magnetic forces exerted on the particle.

Answer 1

Explanation:

It is given that,

Charge, $q=2.4\times 10^{-8}\ C$

Intensity of electromagnetic wave, $I=2.7\times 10^3\ W/m^2$

The intensity of electromagnetic wave is given by :

$I=\dfrac{E^2}{2c\mu_o}$

Where

E is the electric field

$E=\sqrt{2c\mu_o I}$

$E=\sqrt{2\times 3\times 10^8\times 4\pi\times 10^{-7}\times 2.7\times 10^3}$

E = 1426.79 N/C

(a) Electric force, $F=q\times E$

$F=2.4\times 10^{-8}\times 1426.79$

F = 0.000034 N

or

$F=3.4\times 10^{-5}\ N$

(b) As the charge is stationary, v = 0

Magnetic force, $F=qvB=0$

(c) If the charge is moving with speed of, $v=3.7\times 10^4\ m/s$

Electric force, $F=q\times E$

$F=2.4\times 10^{-8}\times 1426.79$

F = 0.000034 N

or

$F=3.4\times 10^{-5}\ N$

(d) Magnetic force, $F=qvB\ sin\theta$

Here, $\theta=90$

Since, $B=\dfrac{E}{c}$

$B=\dfrac{1426.79}{3\times 10^8}=0.0000047\ T$

$F=2.4\times 10^{-8}\times 3.7\times 10^4\times 0.0000047$

$F=4.17\times 10^{-9}\ N$

Hence, this is the required solution.