Biot–Savart law
To illustrate the principles involved, it can be useful to consider the rails and the armature as thin wires or "filaments". With this approximation, the magnitude of the force vector can be determined from a form of the Biot–Savart law and a result of the Lorentz force. The force can be derived mathematically in terms of the permeability constant (formula_7), the radius of the rails (which are assumed to be circular in cross section) (formula_8), the distance between the central axes of the rails (formula_9) and the current (formula_2) as described below.