Question

A stationary particle of charge q = 2.4 × 10-8 C is placed in a laser beam (an electromagnetic wave) whose intensity is 2.3 × 103 W/m2. 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

Given,

q = 2.4 x 10^-8 C ; I = 2.3 x 10^3 W/m^2

a)We know that electric field is related to intensity as:

I = c e0 E^2

E = sqrt (I/c e0)

E = sqrt (2.3 x 10^3/(3 x 10^8 x 8.85 x 10^-12)) = 930.75 N/C

E = 930.75 N/C

F = qE

Fe = 2.4 x 10^-8 x 930.75 = 2.23 x 10^-5 N

Hence, Fe = 2.23 x 10^-5 N

b)we know that

c = E/B => B = E/c

B = 930.75/(3 x 10^8) = 3.103 x 10^-6 T

B = 3.103 x 10^-6 T

Fm = q v B

since charge is stationary, v = 0

Fm = 0

c)v = 3.7 x 10^4 m/s

the electric force is

Fe = q E

Fe = 2.4 x 10^-8 x 930.75 = 2.23 x 10^-5 N

Hence, Fe = 2.23 x 10^-5 N

d)Fm = q v B

Fm = 2.4 x 10^-8 x 3.7 x 10^4 x 3.103 x 10^-6 = 2.76 x 10^-9 N

Hence, Fm = 2.76 x 10^-9 N