It can be derived mathematically in terms of the permeability constant (formula_1), the radius of the rails (which are assumed to be circular in cross section) (formula_2), the distance between the centrepoints of the rails (formula_3) and the current in amps through the system (formula_4) as follows:It can be shown from the Biot-Savart law that at one end of a semi-infinite current-carrying wire, the magnetic field at a given perpendicular distance (formula_5) from the end of the wire is given by::formula_6Note this is if the wire runs from the location of the armature e.g.