# Basic definitions: magnetic flux, inductance,...

## Magnetic flux: definition

Let there be a filiform circuit closed-loop, defined by its contour C and provided with an electric current I.

The magnetic flux Φ associated with the contour C is defined by:

(1)

where:

- is the magnetic field created by the current I
- is the vector element of surface

Stokes' theorem expresses the magnetic flux as a line integral, in the following form:

where:

- is the magnetic vector potential (such as )
- is the vector element of line

## Inductance: definition

The inductance of a filiform circuit closed-loop, defined by its contour C and provided with an electric current I, is defined by the formula:

It can be expressed by one of the two following formulas:

## Self-inductance and mutual inductance

Let i and j be two filiform circuit closed-loops, defined by their contour C_{i}
and C_{j} and flowed through by the electric currents I_{i} and
I_{j}.

The mutual inductance between i and j circuits is defined by the formula:

where Φ_{ij} is the magnetic flux through the closed-loop C_{j}
generated by the magnetic field produced exclusively by the current I_{i}.

With respect to this last definition, the self-inductance of the closed-loop
C_{i} corresponds to the particular case where i = j: