Derivation of self inductance

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

Derivation

where

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.

References

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