ANALYTICAL EXPRESSIONS FOR THE MAGNETIC FIELD OF PRACTICAL COILS

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Abstract

We present a set of new simple closed‐form analytical formulas for the calculation of the magnetic field produced at any point of space by any solid polyhedral conductor with a uniform current density j. The formulas have been obtained by analytical integration of Ampère's law under the only assumptions that the conductor is bounded by flat surfaces and that j = constant in the conductor. This includes bars, bricks, tetrahedrons, wedges, prisms, trapezoids, pyramids, and polyhedrons in general. The formulas contain no singularities, and can be used for the numerical calculation of the field at any point, including points inside the conductor, or on its surface, edges or corners. The formulas can easily be extended for conductors of infinite length. Extensive numerical tests of the formulas have been performed.

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