Question

A stationary particle of charge q = 2.5 × 10^-8 C is placed in a laser beam (an electromagnetic wave) whose intensity is 2.6 × 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

First, we need to find the magnitude of the Electric Field and the Magnetic Field in this electromagnetic wave. By the following two formulas, we can find E and B

Power per unit area = E²/2μ_oc = cB²/2μ_o   where c is the speed of light

So

2.6 X 10³ = E²/(2)(4π X 10^-7)(3 X 10⁸)

E = 1400.13 N/C

2.6 X 10³ = (3 X 10⁸)(B²)/2(4π X 10^-7)

B = 4.67 X 10^-6 T  

Part A) The electric force is F = qE

F = (2.5 X 10^-8)(1400.13)

Electric Force = 3.50 X 10^-5 N which is 35 μN

Part B) The magnetic force, F = qvB

Magnetic force is zero since the charge is not moving

Part C) Exact same as Part A;   the motion has noting to do with the electric force

The electric force is F = qE

F = (2.5 X 10^-8)(1400.13)

Electric Force = 3.5 X 10^-5 N which is 35 μN

Part D)

F = qvB

F = (2.5 X 10^-8)(3.7 X 10⁴)(4.67 X 10^-6)

Magnetic force = 4.32 X 10^-9 N   which is 4.32 nN