Laplace rails and energy conversion

The Laplace rail system

Two parallel conductive rails, connected to a generator, support a movable rod positioned perpendicular to them, which is immersed in a uniform magnetic field B that is itself perpendicular to the plane of the rails. A current I flows through the rod and creates a Laplace force F = ILB, which sets the rod in motion.

Conversion of electrical energy to mechanical energy

This device illustrates the conversion of electrical energy into mechanical energy (mechanical work). When the rod moves at a speed v, an induced electromotive force e = BLv (Faraday’s law) is generated, which partially opposes the current (Lenz’s law): this is the basic principle behind all direct current electric motors.

Application to the electric motor

In a real motor, the rod is replaced by a coil or winding rotating within a magnetic field (often created by magnets or fixed coils, the stator). Laplace’s force acts on each strand of the coil and produces a driving torque that causes the rotor to rotate. The commutator (or an AC power supply) allows the direction of the current to be periodically reversed to maintain a torque oriented in the same direction of rotation.

Common pitfall

It is important to remember that, when the circuit is in motion, a distinction must be made between the Laplace force (due to the applied current) and the induced electromotive force (due to the motion): the two coexist and are linked by a complete energy balance, but they are not calculated in the same way.