Consider a particle of mass m that carries a charge q. Suppose that the particle is

Chapter 6, Problem 41

(choose chapter or problem)

Consider a particle of mass m that carries a charge q. Suppose that the particle is under the influence of both an electric field E and a magnetic field B so that the particles trajectory is described by the path x(t) for a t b. Then the total force acting on the particle is given in mks units by the Lorentz force F = q(E + v B), where v denotes the velocity of the trajectory. (a) Use Newtons second law of motion (i.e., F = ma, where a denotes the acceleration of the particle) to show that ma v = qE v. (b) If the particle moves with constant speed, use part (a) to show that E does no work along the path of the particle. (Hint: Apply Proposition 1.7 of Chapter 3 to v.)