Explanation of results
Current crossing a surface
If the surface of the S area is perpendicular to the current lines and the current density has the same value J at any point on this surface, the electric current crossing the surface is: I = J S
For a surface whose normal 
is
randomly directed with respect to the current density vector, then
the electric current crossing the surface is: 
The current flowing within an undetermined surface will be: 
Dissipated power / losses by Joule effect
The density of the dissipated power (or density of losses by Joule effect) at a point is expressed by means of E and J by the relation:
that can also be written as:
dP = ρ J2 = σE2
The dissipated power (or losses by Joule effect) on a volume region is equal to: 
Electric resistance of a conductor
The electric current flowing through a portion of
a conductor (i element) can be expressed by the relation: 
where:
- Ui is the voltage at the terminals of the conductor element i
- Pi are the losses by Joule effect in the conductor element i
The electric resistance of a portion of a
conductor (element i) can be written as: 
Laplace's force
The force exerted on a non-magnetic conducting region can be calculated by the Laplace's law:
