Detailed derivation of the inductance effect

[DaTario]

Hi All,

Is there any reference that shows in detail how to deduce the inductance effect of a coiled wire, starting from the magnetic influence of each current element $i\, ds$ on the others?

Best wishes,

DaTario

 

[Charles Link]

For a long solenoidal shape, the magnetic field $B$ is readily calculated inside the coil using Ampere's law, as a function of the current $I$. The magnetic flux $\Phi$ can then be computed, and the inductance $L=\frac{\Phi}{I}$. $\\$ Notice also that the EMF $\mathcal{E}=-\frac{d \Phi}{dt}=-L \, \frac{dI}{dt}$. $\\$ For the general case, it is not a simple calculation.

 

[tech99]

The Wheeler empirical formula is often used.
http://home.earthlink.net/~jimlux/hv/wheeler.htm

If we are interested in the characteristics at high frequencies, where distributed capacitance is involved, one of the most readable discussions I have found is here: http://g3rbj.co.uk/wp-content/uploads/2014/07/Self-Resonance-in-Coils.pdf

 

[DaTario]

Thank you Charles and tech99.

Does any of you know the outline of this derivation ? It seems that the outline should have something of a self consistent method (a la Hartree-Fock method in solving the three electron atom, for instance).