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. 
Stokes' theorem has been used.
so that the mutual inductance is a purely geometrical quantity independent of the current in the circuits.
- ^ Jackson, J. D. (1975). Classical Electrodynamics. Wiley. pp. 176, 263.