Which of the following property of a proton can change while it moves freely in a magnetic field? (There may be more than one correct answer.) (a) mass (b) speed (c) velocity (d) momentum
Hint. The magnetic force is always perpendicular to the particle's velocity — think about what that does and doesn't let it change.
Step 1 — Recall the direction of the magnetic force on a moving charge. The magnetic force on a moving charged particle is always perpendicular to its velocity.
Step 2 — Work out the consequence for speed. Since a force perpendicular to motion does no work on the particle, its kinetic energy — and hence its speed — stays constant.
Step 3 — Work out the consequence for velocity and momentum. Even though speed doesn't change, the force continuously changes the direction of motion, so both velocity and momentum (vector quantities depending on direction) do change.
Step 4 — Mass. Mass is unaffected by any of this.
✦ Answer: (c) velocity and (d) momentum can change (in direction); (b) speed and (a) mass stay the same.
Where students slip. Including speed as something that changes — the magnetic force changes only the direction of motion, never the speed, since it does no work on the particle.
