Complete Question
Electromagnetic radiation from a 3.00 mW laser is concentrated on a 2.00 mm2 area. Suppose a 6.00 nC electric charge is in the beam. What is the maximum electric force (in N) it experiences? If the static charge moves at 300 m/s, what maximum magnetic force (in N) can it feel?
Answer:
The value are
[tex]F = 6.378 *10^{-6} \ N[/tex]
and
[tex]F_k = 6.381 *10^{-12} \ N[/tex]
Explanation:
From the question we are told that
The power of the laser is [tex]P = 3.00 mW = 3.00*10^{-3} \ W[/tex]
The area is [tex]A = 2.00 \ mm^2 = 2.0 *10^{-6} \ m^2[/tex]]
The speed is [tex]v = 300 \ m/s[/tex]
The magnitude of the electric charge is [tex]Q = 6.00 nC = 6.00 *10^{-9} \ C[/tex]
Generally the intensity of the beam is mathematically represented as
[tex]I = \frac{P}{A}[/tex]
=> [tex]I = \frac{3.00 *10^{-3}}{ 2.0 *10^{-6}}[/tex]
=> [tex]I = 1500 \ W/m^2[/tex]
Generally the magnitude of the electric field is mathematically represented as
[tex]E_m = \sqrt{\frac{2I}{c \epsilon_o} }[/tex]
Here c is the speed of light with value [tex]c = 3.0*10^{8} \ m/s[/tex]
[tex]\epsilon_o[/tex] is the permittivity of free space with value [tex]\epsilon_o = 8.85*10^{-12} C/(V \cdot m)[/tex]
[tex]E_m = \sqrt{\frac{2 * 1500 }{3.0*10^{8} *8.85*10^{-12} } }[/tex]
=> [tex]E_m = 1063 \ V/m[/tex]
Generally the maximum electric force is mathematically represented as
[tex]F = Q * E_m[/tex]
=> [tex]F = 6*10^{-9 } * 1063[/tex]
=> [tex]F = 6.378 *10^{-6} \ N[/tex]
Generally the intensity of the beam can also be mathematically represented as
[tex]I = \frac{ c * B^2 }{ 2 * \mu_o}[/tex]
Here B is the magnetic field
[tex]\mu_o[/tex] is the permeability of free space with value [tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]
So
[tex]B = \sqrt{\frac{2 * \mu_o * I }{c} }[/tex]
=> [tex]B = \sqrt{\frac{2 * 4 \pi *10^{-7} * 1500 }{3.0*10^{8}} }[/tex]
=> [tex]B = 3.545*10^{-6} \ T[/tex]
Generally the maximum magnetic force is mathematically represented as
[tex]F_k = Q * v * B[/tex]
=> [tex]F_k = 6.00 *10^{-9} * 300 * 3.545*10^{-6}[/tex]
=> [tex]F_k = 6.381 *10^{-12} \ N[/tex]
