5.2 Magnetic Force

Force on a Moving Charge

A moving charge in a magnetic field feels a force given by F = qv × B. The force is always perpendicular to both velocity and field, so it changes direction, not speed — meaning magnetic forces do no work on the charge. Magnitude is F = qvB sin(θ), where θ is the angle between v and B.

Force on a Current-Carrying Wire

A wire carrying current in a magnetic field experiences F = IL × B, where L is the length vector along the current direction. Magnitude is F = ILB sin(θ). Use the right-hand rule: point fingers along current (or v for a positive charge), curl toward B, thumb gives force direction (flip for negative charges).

Circular Motion in a Magnetic Field

Since magnetic force is always perpendicular to velocity, it acts as a centripetal force, producing circular motion when v ⊥ B: qvB = mv²/r, giving radius r = mv/(qB). This principle underlies devices like mass spectrometers and cyclotrons.

Key terms

Magnetic force on a moving charge

F = qv × B; magnitude F = qvB sin(θ), direction found via right-hand rule.

Magnetic force on a current-carrying wire

F = IL × B; magnitude F = ILB sin(θ), where L points along current direction.

Why magnetic force does no work

It's always perpendicular to velocity, so it changes direction but never speed or kinetic energy.

Radius of circular motion in a magnetic field

r = mv/(qB), derived by setting magnetic force equal to centripetal force.

Right-hand rule (positive charge)

Point fingers along v, curl toward B; thumb points in direction of F. Reverse for negative charges.

Try an AP-style question

A proton moves at v = (2 × 10⁵ m/s)î through B = (0.5 T)ĵ. Which way does the force point?

1. +î
2. +k̂ (out of the page)
3. −ĵ
4. −k̂ (into the page)