Harman Patil (Editor)

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

M i j = μ 0 4 π C i C j d s i d s j | R i j |

Derivation

Φ i = S i B d a = S i ( × A ) d a = C i A d s = C i ( j μ 0 I j 4 π C j d s j | R | ) d s i

where

Φ i   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.

M i j   = d e f   Φ i I j = μ 0 4 π C i C j d s i d s j | R i j |

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

References

Derivation of self inductance Wikipedia


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