Flux coordinates: Difference between revisions
→Covariant Form
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[[Image:CurrentIntegrationCirtuitsPoloidalCurrent.png|256px|thumb|right|alt=Sample surface for the definition of the current though a disc.|Sample surface for the definition of the current though a disc. Note that only the current of more external surfaces contribute to the flux of charge through the surface.]] | [[Image:CurrentIntegrationCirtuitsPoloidalCurrent.png|256px|thumb|right|alt=Sample surface for the definition of the current though a disc.|Sample surface for the definition of the current though a disc. Note that only the current of more external surfaces contribute to the flux of charge through the surface.]] | ||
The functional dependence on the angular variables is again motivated by the single-valuedness of the magnetic field. The particular form of the coefficients can be obtained noting that | Note that <math>I</math> is not the current but <math>\mu_0</math> times the current. The functional dependence on the angular variables is again motivated by the single-valuedness of the magnetic field. The particular form of the coefficients can be obtained noting that | ||
:<math> | :<math> | ||
\int_S \mu_0\mathbf{j}\cdot d\mathbf{S} | \int_S \mu_0\mathbf{j}\cdot d\mathbf{S} | ||