(a) Write a computer program that displays a sinusoidal electromagnetic wave propagating through space. Make the
wavelength 600 m (corresponding to a frequency of about 500 kHz, which is in the AM radio frequency band) and
the amplitude of the electric field 1.0 × 104 V/m. (This is roughly the amplitude that would be measured a few
meters from a 50,000W radio transmitter. On average, the amplitude of the radiative field from the Sun at Earth's
orbital radius is about 700 V/m.)
Animate the wave as a function of time, making it propagate in the positive x direction, with the electric field
polarized in the y direction. Display both the electric and magnetic field vectors, and make sure they have the
correct directions relative to each other. Display at least 3 full wavelengths, with enough observation locations per
wavelength that you can clearly see the sinusoidal character of the wave. Think carefully about scaling. The length
of the arrow objects must be scaled such that both the arrows and the wavelength can be seen. Also, to see smooth
wavelike motion, the time step must be a small fraction of the period of the wave.
(b) Place a positron initially at rest in the presence of the electromagnetic wave from part (a). (Using a positron instead
of an electron makes it easier to think about signs and directions.) Modify your program to model the motion of the
positron due to its interaction with the electromagnetic wave. Leave a trail. This is a relativistic situation since the
instantaneous speed of the particle can get quite high. To accurately model the positron's motion, you'll need to use
the relativistic relationship between momentum and velocity: