The calculation of the magnetic attraction between two coils, carrying current, is subject closely related to the calculation of their mutual inductance. Since their mutual energy is equal to the product of their mutual inductance by the currents in the coils, the component of the magnetic force (attraction or repulsion) in any direction is equal to the differential coefficient of the mutual inductance, taken with respect to that coordinate, and multiplied by the product of the currents. Evidently the force may be calculated by simple differentiation in any case where a general formula for the mutual inductance is available, expressed as function of coordinate along which the force is requested, [1].
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