The Theory of Experimental Electricity

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The resultant magnetic force of any circuit is equal to the sum of the forces due to its individual rational current elements.
We may therefore use Ampere's formula to calculate the magnetic effects of different currents, whether those currents be continuous ones carried in conductors, or the nights of charged particles which have become recently of so much importance.
Ampere's formula may also be applied to calculate the mechanical forces between circuits, or circuits and magnets. The magnetic
... V] THE ELECTRIC CURRENT 105 force due to the current element being cBl sin 0/r 2, and that due to a magnetic pole of strength ra being ra/r 2, it follows from the principle of equivalence between currents and magnets that cBl sin is equivalent to ra. Now if a pole ra be placed in a magnetic field where the induction is B, the mechanical force on it is Em. Thus on the current element the me- chanical force is Be U sin 6, the direction of the force being at right angles both to the current and to the lines of induction, and 6 de- noting the angle between the lines of induction and the direction of the current.

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