4.2 Magnetic Fields and Forces on Moving Charges

Force on a moving charge

A charged particle moving through a magnetic field (B) feels a force given by F = qvB sin θ, where θ is the angle between velocity and B. The force is zero if the charge is stationary or moves parallel to B, and maximum when velocity is perpendicular to B.

Direction: the right-hand rule

The magnetic force is always perpendicular to both velocity and B, so it never changes speed—only direction. For a positive charge, point fingers along v, curl toward B; thumb gives F (right-hand rule). For negative charges, reverse the direction.

Circular motion in a magnetic field

Since F is always perpendicular to v, a charged particle entering a uniform B field perpendicular to its velocity moves in a circle. Setting magnetic force equal to centripetal force: qvB = mv²/r, so r = mv/(qB). Faster or more massive particles curve in bigger circles; stronger fields or charges curve tighter.

Key terms

Magnetic force equation

F = qvB sin θ, where θ is the angle between velocity v and magnetic field B.

Right-hand rule (positive charge)

Point fingers along v, curl toward B; thumb points in direction of F = qv × B.

Why speed stays constant in a magnetic field

Magnetic force is always perpendicular to velocity, so it does no work and only changes direction.

Radius of circular motion

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

Force on a stationary charge in B field

Zero — magnetic force requires the charge to be moving (F = qvB sin θ = 0 when v = 0).

Try an AP-style question

A charge moves parallel to a uniform magnetic field. What magnetic force acts on it?

1. qvB
2. qvB/2
3. Zero
4. It depends on its mass