Chapter 3

# Laplace's force

## Fondamental : Case of parallelepiped conductor

This lesson uses the same notations as the lesson about Hall effect.

The following video shows the Laplace's force experimentally (Alain Le Rille, CPGE teacher at lycee Janson de Sailly, Paris)

Laplace force (Alain Le Rille, CPGE teacher at lycée Janson de Sailly, Paris)

What is the expression of the force applied by the magnetic field to the conductor ?

The set of carrier electrons and metallic cations in the conductor is subject to the following forces due to the magnetic field :

• On the carrier electrons :

Where is the density of charge carriers.

• On metallic cations (still) :

Globally the conductor is subject to the force :

The Laplace's force on a parallelepiped conductor

The intensity can be expressed as:

So :

## Attention : Laplace's force for a thread-like conductor

A portion of the thread-like circuit is travelled by the intensity and put in a certain magnetic field .

Laplace's force on a thread-like conductor

The conductor is subject to the force called Laplace's force :

By writing :

Then :

This is the expression of the Laplace's force for volume currents.

Differences between Laplace's and Lorentz's forces :

• Lorentz's force is microscopic. It is applied to charge moving carriers in a magnetic field :

• Laplace's force is macroscopic. It is applied to any conductor, electrons and cations included.

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