Force on a Current-Carrying Wire
When a wire carrying electric current is placed in an external magnetic field, it experiences a force perpendicular to both the current direction and the magnetic field. This is a macroscopic manifestation of the Lorentz force acting on the moving charge carriers (electrons) in the wire. The force direction is determined by the right-hand rule or Fleming's left-hand rule.
This force is the operating principle behind electric motors, loudspeakers, and galvanometers. By passing current through a wire or coil in a permanent magnet's field, continuous rotational or linear motion can be produced. The force is maximum when the wire is perpendicular to the field and zero when parallel to it.
The Formula
Where F is the force (N), I is current (A), L is wire length (m), B is magnetic field (T), and θ is the angle between the wire and the field.
Applications
| Device | Principle | Typical Force |
|---|---|---|
| DC Motor | Rotating coil in B field | 0.1-1000 N |
| Loudspeaker | Voice coil in radial B | 0.01-10 N |
| Galvanometer | Coil deflection | μN range |
| Railgun | Armature in B field | MN range |
Frequently Asked Questions
Why is the force maximum at 90 degrees?
The cross product F = IL x B has maximum magnitude when L and B are perpendicular (sin 90 = 1). When the wire is parallel to B (0 or 180 degrees), the Lorentz force on each charge carrier is along the wire and cannot produce a net force on the wire. Only the component of velocity perpendicular to B contributes to the sideways force.
How does a DC motor use this force?
A DC motor has a coil mounted on an axle (rotor) inside a permanent magnet (stator). Current flowing through the coil creates forces on opposite sides in opposite directions, producing torque. A commutator reverses the current direction every half turn to maintain continuous rotation. The torque is proportional to NIAB, where N is the number of turns.
What is the force on a curved wire?
For a curved wire in a uniform field, only the straight-line distance between the endpoints matters. The force equals F = IL_eff B sin(θ), where L_eff is the length of the straight line connecting the wire's start and end points. This is because the contributions from curved segments cancel out in a uniform field.