Questions: Lorentz Force on Moving Electric Charges

Question 1

A proton enters a uniform magnetic field moving at constant speed. Which of the following CANNOT be caused by the magnetic force alone?

• A. The proton's direction of travel changes
• B. The proton moves in a circular arc
• C. The proton's speed increases
• D. The proton follows a helical path along a field line

Answer: (C)

The magnetic force is always perpendicular to the velocity, so the dot product F·v = 0 — the force does no work. Since kinetic energy = ½mv², and no work is done, speed cannot change. The magnetic force can only redirect the particle: it causes circular motion (when v ⊥ B), helical motion (when v has components both perpendicular and parallel to B), or direction changes generally. It is purely a steering force.

Question 2

An electron moves to the right through a region where the magnetic field points into the page. The right-hand rule applied to v × B gives an upward direction. In which direction does the magnetic force on the electron point?

• A. Upward — the right-hand rule determines the force direction regardless of charge sign
• B. Downward — the force on a negative charge reverses compared to a positive charge
• C. Into the page — the force is parallel to the field
• D. To the right — the force is parallel to the velocity

Answer: (B)

The Lorentz force is F = q(v × B). The right-hand rule gives the direction of v × B, which is upward here. For a positive charge, F is upward. For a negative charge (the electron), q is negative, so F = q(v × B) reverses direction — the force is downward. The key: always find v × B first with the right-hand rule, then flip the direction if the charge is negative.

Question 3

A stationary electric charge placed inside a strong magnetic field experiences no magnetic force.

• T. True
• F. False

Answer: True

The magnetic force law is F = q(v × B). If v = 0 (the charge is stationary), then v × B = 0, so F = 0. Motion is essential — the magnetic force acts only on moving charges. This distinguishes it fundamentally from the electric force, which acts on charges regardless of whether they move.

Question 4

A magnetic force can accelerate a charged particle — that is, increase its kinetic energy — if the field is strong enough.

• T. True
• F. False

Answer: False

No matter how strong the magnetic field, the magnetic force is always perpendicular to the velocity. Since power = F · v and the dot product of perpendicular vectors is zero, the magnetic force does zero work at every instant. Kinetic energy (½mv²) cannot change. Magnetic forces change direction but never speed. This is why particle accelerators use electric fields (which can do work) to speed particles up, while magnetic fields are used to steer them.

Question 5

Why does a charged particle moving perpendicular to a uniform magnetic field follow a circular path at constant speed? Explain using the force law.

Model answer: The magnetic force F = qvB is always perpendicular to the velocity, so it provides centripetal acceleration without doing work. This means the speed stays constant while the direction continually changes — which is exactly the definition of uniform circular motion. Setting the magnetic force equal to the centripetal force: qvB = mv²/r gives the cyclotron radius r = mv/(qB). The particle curves continuously because the force always points toward the center of the circle.

The key physical insight is that a force perpendicular to velocity acts as a centripetal force: it bends the trajectory without changing the magnitude of velocity. The resulting orbit has a radius that depends on the particle's momentum mv and the field strength qB — a stronger field means tighter bending. This is the operating principle of cyclotrons and particle beam steering magnets.