Astationary particle of charge q = 2.1 × 10-8 c is placed in a laser beam (an electromagnetic wave) whose intensity is 2.9 × 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.

(a) The intensity of the electromagnetic wave is related to the amplitude of the electric field by

where
I is the intensity
c is the speed of light
is the electric permittivity
E is the amplitude of the electric field

By substituting the numbers of the problem and re-arranging the equation, we can find E:


Now that we have the intensity of the electric field, we can calculate the electric force on the charge:


(b) We can calculate the amplitude of the magnetic field starting from the amplitude of the electric field:


The magnetic force is given by

where v is the particle's speed, B the magnetic field intensity and  the angle between B and v.
In this case the charge is stationary, so v=0, and so the magnetic force is zero: F=0.

(c) The electric force has not changed compared to point (a), because it does not depend on the speed of the particle, so we have again F=0.046 N.

(d) This time, the particle is moving with speed , in a direction perpendicular to the magnetic field (so, the angle  is ), and so by using the intensity of the magnetic field we found in point (b), we can calculate the magnetic force on the particle: