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Re: Inductance and the acceleration of charge



Original poster: Terrell Fritz <terrellfone@xxxxxxxxxxxxxxxxxxxxxxx>

Hi,

Yeah!  Get that all worked out and report back :o))

The best measure of inductance is a darn good metering system...

The second is a darn good program...

The third is a darn good equation about 100 years old beginning with the name "Wheeler's"...

There are "no" others...

Cheers,

        Terry


At 03:10 PM 2/12/2007, you wrote:
Original poster: "Jared Dwarshuis" <jdwarshuis@xxxxxxxxx>

Inductance and  the acceleration of charge

We can take the classic equation for inductance:

  L = u Nsqrd Area / Height

We can multiply the numerator and denominator by (4 pi), regroup and get:

  L = u (wire length)sqrd / (4 pi) Height.

 We can use the fact that C = 1 / sqrt (u e) and write:

  L = (wire length / C) sqrd    1/ (four pi)   e  Height

The denominator of the last expression ( 1/ 4pi e H) reveals an inverse capacitance. But there is also a relationship between H and radius.

For a given length of wire, we can wind a long skinny coil where H is large but radius is small. The inductance will be small for this arrangement.

We could alternately wind a fat coil with our fixed wire length. This would give us a small H. In this instance our radius will be large and our inductance will be large.

In a nutshell, as the radius of our inductor increases (for a given wire length) the inductance also increases.

Partial physical interpretation:

Charge is traveling in a circular path at the fixed velocity of C. The charge has a relativistic mass. As we increase the radius of our inductor for a given wire length, we increase the moment of inertia. As the system inertia increases so does the inductance.

We are still in the process of examining the relationships above, (tying them to the Lorentz forces) and are inviting intelligent remarks!

Sincerely: Jared Dwarshuis, Larry Morris