4.3 Force on a Current-Carrying Conductor

Force on a current-carrying wire

A wire carrying current I in a magnetic field B feels a force given by F = BIL sin(θ), where L is the length of wire in the field and θ is the angle between the current direction and B. Force is maximum when the wire is perpendicular to B (θ = 90°) and zero when parallel (θ = 0°).

Direction: the right-hand rule

Point fingers in the direction of conventional current I, curl them toward B, and your thumb (for cross product F = IL × B) points in the direction of F. This force is always perpendicular to both the current and the magnetic field — it never does work on the charges in the sense of changing their speed along the field, only redirecting them.

Applications: rails and loops

Parallel current-carrying wires exert forces on each other — attract if currents are parallel, repel if antiparallel — because each wire's current interacts with the other's field. Current loops in a magnetic field experience forces on opposite sides that can create a torque, the basis for motors.

Key terms

Force on a current-carrying wire formula

F = BIL sin(θ), where I = current, L = length in the field, B = magnetic field, θ = angle between I and B.

When is force on a wire maximum?

When the wire is perpendicular to the magnetic field (θ = 90°), giving F = BIL.

When is force on a wire zero?

When the current is parallel or antiparallel to B (θ = 0° or 180°).

Right-hand rule for wire force

Point fingers along current direction, curl toward B; thumb gives direction of force F.

Parallel currents in same direction

Attract each other; opposite directions repel — basis for defining current force interactions.

Try an AP-style question

A 0.5 m wire carrying 2 A is perpendicular to a 0.3 T field. What is the magnetic force?

1. 0.03 N
2. 3 N
3. 0.3 N
4. 1.2 N