# Electromagnetic induction

# Power of the induced electromotive force and the Laplace's force

### Fondamental :

A charge carrier is put in a permanent magnetic field.

It moves with a velocity in relation to the conductor, but the conductor moves at velocity in the laboratory referential .

In this referential, the charge carrier has a speed ( ) and is subject to Lorentz's Force :

Yet its power is equal to zero :

This power can be separated in 4 terms, and two of them are equal to zero :

In an elementary volume , the number of charge carriers is .

The density of power of Lorentz's force is :

The term :

represents the density of power of the force applied to the charges because of the electromotive field .

This density is evaluated in the referential of the conductor.

By adding it on the whole volume of the conductor, the power of the induced electromotive force is found :

Interpretation of the term :

This term appears to be the power of Laplace's force applied to elementary volume .

Finally, after integration :

The power of the induction electromotive force is compensated by that of the actions of the Laplace's force on the circuit.

### Attention : Power of induced electromotive force and Laplace's force

The power of the induction electromotive force is compensated by that of the actions of the Laplace force on the circuit.