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Derivation of self inductance
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Derivation of self inductance : ウィキペディア英語版
Derivation of self inductance
The mutual inductance by circuit ''i'' on circuit ''j'' is given by the double integral ''Neumann formula''
: M_ = \frac \oint_\oint_ \frac_j}|}
==Derivation ==
: \Phi_ = \int_ \mathbf\cdot\mathbf = \int_ (\nabla\times\mathbf)\cdot\mathbf
= \oint_ \mathbf\cdot\mathbf = \oint_ \left(\sum_\frac \oint_ \frac\right) \cdot \mathbf_i
where
:\Phi_i\ \, is the magnetic flux through the ''i''th surface by the electrical circuit outlined by ''C''''j''
:''Ci'' is the enclosing curve of S''i''.
:''B'' is the magnetic field vector.
:''A'' is the vector potential.
Stokes' theorem has been used.
: M_ \ \stackrel\ \frac = \frac \oint_\oint_ \frac_j}|}
so that the mutual inductance is a purely geometrical quantity independent of the current in the circuits.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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