Flux coordinates: Difference between revisions

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\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(\beta\nabla\psi + \nabla\chi)\cdot d\mathbf{l}
= \oint(-\eta\nabla\psi + \nabla\chi)\cdot d\mathbf{l}
= \oint(\beta d\psi + d\chi)
= \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
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