Question

Electromagnetic radiation from a 8.25 mW laser is concentrated on a 1.23 mm2 area. Suppose a 1.12 nC static charge is in the beam, and moves at 314 m/s. What is the maximum magnetic force it can feel

Answer 1

The maximum magnetic force is 2.637 x 10⁻¹² N

Step-by-step explanation:

Given;

Power, P = 8.25 m W = 8.25 x 10⁻³ W

charge of the radiation, Q = 1.12 nC = 1.12 x 10⁻⁹ C

speed of the charge, v = 314 m/s

area of the conecntration, A = 1.23 mm² = 1.23 x 10⁻⁶ m²

The intensity of the radiation is calculated as;

`I = (P)/(A) \\\\I = (8.25 * 10^(-3) \ W)/(1.23 \ * 10^(-6) \ m^2) \\\\I = 6,707.32 \ W/m^2`

The maximum magnetic field is calculated using the following intensity formula;

`I = (cB_0^2)/(2\mu_0) \\\\B_0 = \sqrt{(2\mu_0 I)/(c) } \\\\where;\\\\c \ is \ speed \ of \ light\\\\\mu_0 \ is \ permeability \ of \ free \ space\\\\B_0 \ is \ the \ maximum \ magnetic \ field\\\\B_0 = \sqrt{(2 * 4\pi * 10^(-7) * 6,707.32 )/(3* 10^8) } \\\\B_0 = 7.497 * 10^(-6) \ T`

The maximum magnetic force is calculated as;

F₀ = qvB₀

F₀ = (1.12 x 10⁻⁹) x (314) x (7.497 x 10⁻⁶)

F₀ = 2.637 x 10⁻¹² N