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The following notation is used throughout the report:

A derivation of Grassmann's law

Biot-Savart's law, well known from magnetostatics, gives the magnetic field from a circuit:


tex2html_wrap_inline3123 is the magnetic field; tex2html_wrap_inline2997 the electric current; tex2html_wrap_inline2993 is an infinitesimal section of the conductor; tex2html_wrap_inline3007 the distance from tex2html_wrap_inline2993 to the point where the magnetic field is to be measured,; and tex2html_wrap_inline3009 the unit vector from tex2html_wrap_inline2993 to that point.

In differential form it becomes:


The magnetic force ( tex2html_wrap_inline3259 ) that moving charge experiences in a magnetic field is given by the Lorentz force law:


Here q is the charge that is moving; tex2html_wrap_inline3523 its velocity; and tex2html_wrap_inline3121 the magnetic induction. With tex2html_wrap_inline3527 in vacuum (and air), and noting that tex2html_wrap_inline3529 we have:


which is Grassmann's law for the force between two current elements.

Lars Johansson, Email: forename.surname@newphys.seSeptember 19:th, 1996