Laplace’s force and its applications

Laplace’s force

When a conductor carrying a current I is placed in an external magnetic field B, it experiences a force known as Laplace’s force, denoted by F. For a wire of length L placed perpendicular to the field B, the magnitude of this force is given by:

F = B * I * L

F is expressed in newtons (N), B in teslas (T), I in amperes (A) and L in metres (m). If the wire is parallel to the field, the force is zero.

Direction of the Laplace force

The direction of F is given by the right-hand rule: the thumb indicates the direction of the current, the index finger indicates the direction of the field B, and the middle finger (perpendicular to the other two) then indicates the direction of the force F.

Applications

Application	Principle used
Electric motor	Laplace’s force on a turn of wire in a rotating field
Loudspeaker	Laplace’s force on a moving coil
Laplace’s rail	displacement of a conducting rod on rails

Common pitfall

The Laplace force exists only if the current and the magnetic field are not parallel. If I = 0 (open circuit) or if B = 0, then F = 0: always check these conditions before applying the formula. Also, remember that F is perpendicular to both I and B, which explains the motion observed in an electric motor.