Question

1. A particle of positive charge q and mass m enters parallel uniform electric and magnetic fields (of magnitudes E and B, respectively) both directed in the +z direction with a velocity v = v₀i perpendicular to both fields.

(a) What is the the particle’s initial acceleration? You can give your answer as a vector in component form.

(b) What is the radius of the particle’s path (looking down the z-axis) if the magnetic field is B = Bk? Does it depend on time?

(c) How does the pitch, p(z), of the particle’s path vary with its z-axis coordinate? Let the electric field be given by E = Ek. Assume that the particle enters the field in the x, y-plane (at z = 0) and let p(z) = v_z(z)T(z) where T(z) is the time period of a single orbit, and v_z(z) is the component of the velocity along the z-direction.

Answer 1