Inductance and the acceleration of charge

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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