Whats the real definition of inductance?

[apchar]

My old freshman physics text defined inductance as flux/turns, which applies only to solenoids. This seems like a pretty weak definition since any length of wire in any geometry has some inductance. There has to be a more general definition.
My first guess was that L could be calculated from the energy in the magnetic field:
volume integral of B^2/2mu0 = 1/2 L I^2
(sorry but the latex engine is acting weird)
You can numerically get B from just slow-but-simple Biot-Savart's law.
But I tried this for a simple circular loop of infinitesimally thin wire and got a squirreley (wrong) answer. The code is fine. I verified the calculated B for some known geometries. So I guess I'm on the wrong track.
So what's the real definition of inductance for an arbitrary current distribution?

 

[dlgoff]

http://en.wikipedia.org/wiki/Inductance"

 

[apchar]

http://en.wikipedia.org/wiki/Inductance"

That's too macroscopic. It treats the inductor as a black box. I can build all manner of 1 port circuits that resist a change in the current flow but that doesn't make them inductors. I'm looking for a definition based on the physics.

 

[dlgoff]

Too macroscopic? Did you read the link?

Anyway, http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html" says it all.

 

[f95toli]

That's too macroscopic. It treats the inductor as a black box. I can build all manner of 1 port circuits that resist a change in the current flow but that doesn't make them inductors. I'm looking for a definition based on the physics.

Yes it does, inductance is a property of a circuit element; HOW you get a specific inductance is not important.
Remember that just about all real circuit elements are inductive (many capacitors become inductive at high frequencies. and vice versa).
There is no such thing as a "pure" inductor, it is just a concept we use when me create mathematical models of real circuits (and those models are only valid for a certain range of frequencies) meaning there is no way to "define" it based on physics.
Also, there are all sorts of "exotic" inductances that are nevertheless real (=can be read out using an RCL meter). Good examples relevant for the work I do would be kinetic inductance and Josephson inductance.

 

[jonlg_uk]

Think of it like this:

If a source of electric power is suddenly applied to an unmagnetized inductor, the inductor will initially resist the flow of electrons by dropping the full voltage of the source. As current begins to increase, a stronger and stronger magnetic field will be created, absorbing energy from the source. Eventually the current reaches a maximum level, and stops increasing. At this point, the inductor stops absorbing energy from the source, and is dropping minimum voltage across its leads, while the current remains at a maximum level. As an inductor stores more energy, its current level increases, while its voltage drop decreases. Note that this is precisely the opposite of capacitor behavior, where the storage of energy results in an increased voltage across the component. Whereas capacitors store their energy charge by maintaining a static voltage, inductors maintain their energy "charge" by maintaining a steady current through the coil.

Therefore the measure of an inductor's ability to store energy for a given amount of current flow is called inductance.

 

[sophiecentaur]

It treats the inductor as a black box. . . . . . . I'm looking for a definition based on the physics.

An inductor IS a black box concept and it only refers to the simplest way of describing the way a component behaves over a certain band of frequencies. For instance, for an object with dimensions which are a significant fraction of a wavelength (and antenna or transmission line) the Impedance (including reactance / inductance) is frequency dependent. Also, even a humble wound inductor will have significant inter-winding capacity and this contributes to its measured / effective inductance at all frequencies.