Consider the motion of a particle with mass m and electric charge q_e in the field of a (hypothetical) stationary magnetic monopole qm at the origin:

(a) Find the acceleration of qe, expressing your answer in terms of q, qm, m, r (the position of the particle), and v (its velocity). 

(b) Show that the speed v --- Ivl is a constant of the motion. 

(c) Show that the vector quantity is a constant of the motion.

(d) Choosing spherical coordinates (r, θ, Ф), with the polar (z) axis along Q, (i) calculate Q ∙ Ф, and show that θ is a constant of the motion (so qe moves on the surface of a cone--something Poincare first discovered in 1896)¹⁸;