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value for the field found above.

Mathematical formulation

In a more mathematical vein, the same results can be obtained from the underlying differential equations. Consider for simplicity a non-magnetic medium where the relative magnetic permeability is unity, and the complication of magnetization current (bound current) is absent, so that and 1=$\backslash mathbf\{J=\; \backslash mathbf\{J\}\_\backslash mathrm\{f\}$.}}The current leaving a volume must equal

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