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Re: Inductance and the acceleration of charge



Original poster: mercurus2000 <mercurus2000@xxxxxxx>

Are you trying to say charges and electrons in the inductor are accelerating since they are moving in a circular path? That is correct, but the charge doesn't travel at relativistic velocities in the wire tho.
Adam
Tesla list 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