Derivation of self inductance

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The mutual inductance by circuit i on circuit j is given by the double integral Neumann formula



is the magnetic flux through the ith surface by the electrical circuit outlined by Cj
Ci is the enclosing curve of Si.
B is the magnetic field vector.
A is the vector potential. [1]

Stokes' theorem has been used.

so that the mutual inductance is a purely geometrical quantity independent of the current in the circuits.


  1. ^ Jackson, J. D. (1975). Classical Electrodynamics. Wiley. pp. 176, 263.