Consideration of the relationship between the magnetic field produced by a magnetic shell and that produced by a current loop requires the evaluation of the line integral ɸH̅ • dl̅, where a portion of the path must cross the dipole layer. The correct line integral to be evaluated must be ɸB̅ • dl̅. The evaluation of this integral leads immediately to the correct Maxwell equation in ∆ x H̅. Gaussian units are used.

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