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The following notation is used throughout the report:
Biot-Savart's law, well known from magnetostatics, gives the magnetic field from a circuit:
is the magnetic field; the electric current; is an infinitesimal section of the conductor; the distance from to the point where the magnetic field is to be measured,; and the unit vector from to that point.
In differential form it becomes:
The magnetic force ( ) that moving charge experiences in a magnetic field is given by the Lorentz force law:
Here q is the charge that is moving; its velocity; and the magnetic induction. With in vacuum (and air), and noting that we have:
which is Grassmann's law for the force between two current elements.