A constant uniform magnetic induction B in the negative z direction exists in a region limited by the planes x=0 and x=a. For x<0 and x>a, there is no magnetic induction.
(a) Determine the total electromagnetic momentum G in magnitude and direction of the combination of a particle with point charge q at (x0,y0,z0) in the presence of this magnetic induction. Find G for the charge located on either side of and within the region occupied by the magnetic field. Assume the particle is at rest or in nonrelativistic motion.
(b) The particle is normally incident on the field region from x<0 with nonrelativistic momentum p. Assuming that p>qBa/c, determine the components of momentum after the particle has emerged into the field-free region, x>a. Compare the components of the sum of mechanical (particle) and electromagnetic momenta initially and finally. Why are some components of the sum conserved and some not?
(c) Assume that p<qBa/2c and that the initial conditions are such that the particle's motion is confined within the region of the magnetic induction at fixed z. Discuss the conservation, or lack of it, of the components of the sum of mechanical and electromagnetic momentum as the particle moves in its path. Comment.