# 2D example: computation of Laplace's electromagnetic force

## Introduction

This section depicts the computation of the mean and pulsating components of Laplace's force in 2D.

## Definition: reminder

The Laplace's electromagnetic force is the force exerted on a conducting conductor placed in a magnetic field.

## Mathematical expression

The force exerted on a conductor can be computed using Laplace's law:

where:

- is the magnetic flux density in which the conductor is placed
- is the current density in the conductor

## Expression of the mean and pulsating components of Laplace's force

The magnetic flux density and the current density in a point are expressed in the following way:

- Magnetic flux density is written:

That is the parametric equation of an ellipse (see the figure beside)

- the current density is written:

Thus , the expression of the Laplace's force in a point is:

## Expression of the mean and pulsating components (continued)

Hence, the Laplace's force is constituted by:

- a mean component :
- a pulsating component :

## Elliptical representation

The force can be spatially represented as that in the figure below.

- The mean component
is defined by:
- its modulus and its orientation with respect to the Ox axis(
**α**angle)

- its modulus and its orientation with respect to the Ox axis(

- The pulsating component described by an ellipse of
**2ω**pulsation:- major axis:
**a** - minor axis:
**b** - orientation of the ellipse with respect to the Ox (
**β**angle)

- major axis: