IB Physics Work Done on a Moving Charge in a Magnetic field

A common question is finding the work done on a charge as it moves in a magnetic field. Is it always zero? A tutorial sheet of questions investigates this concept.

  1. A constant, uniform magnetic field B acts along the x-axis. A charge q enters the field at a velocity v at an angle 𝜃 to the x-axis. Is work done on the moving charge?
  2. A constant current flows along a long straight wire that is along the x-axis. At a certain instant a charge q is moving along the x-axis at a speed v towards the wire. Is work done on the charge?
  3. A magnetic field increases at a rate proportional to the time, B = kt, and its direction is parallel to the x-axis. Does the magnetic field do work on the moving charge in question 1? Does the associated electric field do work on the moving charge?