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Beginning with expressions for the vector potential, the equations for calculating the magnetic flux density from up to three rectangular loops of wire in the same plane are derived. The geometry considered is the same as that found in some walk-through metal detectors and electronic article surveillance systems. Equations for more or fewer loops can be determined by inspection. A computer program for performing the magnetic field calculation is provided in an appendix.

Equations for the magnetic field produced by one or more rectangular loops of wire in the same plane