204
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Flux coordinates: Difference between revisions
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→Covariant Form
| Line 192: | Line 192: | ||
\int_S \mu_0\mathbf{j}\cdot d\mathbf{S} | \int_S \mu_0\mathbf{j}\cdot d\mathbf{S} | ||
= \int_{\partial S}\mathbf{B}\cdot d\mathbf{l} | = \int_{\partial S}\mathbf{B}\cdot d\mathbf{l} | ||
= \oint(\ | = \oint(-\eta\nabla\psi + \nabla\chi)\cdot d\mathbf{l} | ||
= \oint(\ | = \oint(-\eta d\psi + d\chi) | ||
</math> | </math> | ||
and choosing an integration circuit contained within a flux surface <math>(d\psi = 0)</math>. Then we get | and choosing an integration circuit contained within a flux surface <math>(d\psi = 0)</math>. Then we get | ||