inductance on the microscopic level inquiry

[azaz104]

Hey all,
for all you physic veterans, i know this may come easy to you, but for
electrical engineers, the things may not come as easy.
My question lies within the area of inductor/inductance analysis.
although I know nothing about quantum physics, but I would appreciate someone giving a scientific explanation, with strong mathematics about looped wires with sinusoidal currents passing through them, not the all time explanation that inductors' reactance increases with frequency, and lenz's law.......
can anyone point me to a good article - long elaborating one- about this.

-Bassel

 

[Jone]

So what would excatly like to know? What inductance is?

 

[azaz104]

an inductor on the "electron level"

why does it behave like that..
that is why the relationship between I and V is as it is
physically and not logically

 

[Jone]

Well, inductance is not really defined from an "electron" point of view, altough you could do it in a similar way as with macroscopic pheomonena.

You run a steady current in a loop of wire and this will induce a flux in any nearby loop. From the Biot-Savart law we see that flux through the second loop is propotional to the current in the first loop; phi = M*I, M = mutual inductance. If the current is changing, the flux will also change and we will have an emf in the loop (Faraday's law). But this loop also induces flux in the source loop itself and the constant of proportionality is now called (self-)inductance, phi = LI. In physics one often looks for simple relations, so that we can define some proportionality constant. After then we try to explain what this constant means physically. This is not always so easy. For the case with inductance it is maybe most easily understood from emf = -LdI/dt; The greater the inductance, the harder is it to change the current.

Inductance ís really something defined from at an macroscopic level. However, when materia is involved (like an inductor with ferromagnetic material) it gets more complicated. To really understand what happens you need quantum mechanics. Magnetic material is complicated.

 

[azaz104]

actually what I really need to know is that why a flux is created and HOW it is sensed by the other coil
now..why is it that a current generates it ?
and How...please can you elaborate?

 

[Jone]

A current in a wire creates electric and magnetic fields around it. These fields are forces which act on charges. This is stated by the Lorentz force law:

F = q(E+vxB).

This is a fundamental law or an axiom of electromagnetics, verified by experiments and cannot be derived. You cannot derive something from nothing; One observe some fundamental phenomena in the nature and state a law. So the whole theory of EM begins with the Lorentz force law.
You've probably seen the following schenario before where a loop is pulled in a constant magnetic field.

The Lorentz force becomes F = qvB, in a direction down. Emf is defined as the total force/charge and becomes emf = vBh = -dx/dt*B = -d(Bhx)/dt = -dΦ/dt. If the magnetic field instead changes because of a changing current one obtains the same results. So the loop senses these fields just like a stone senses the gravitational field and hence falls down towards the earth.