[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*To*: tesla@xxxxxxxxxx*Subject*: Re: Wire length LC derivation,*From*: "Tesla list" <tesla@xxxxxxxxxx>*Date*: Sun, 13 Mar 2005 22:27:20 -0700*Delivered-to*: testla@pupman.com*Delivered-to*: tesla@pupman.com*Old-return-path*: <teslalist@twfpowerelectronics.com>*Resent-date*: Sun, 13 Mar 2005 22:28:51 -0700 (MST)*Resent-from*: tesla@xxxxxxxxxx*Resent-message-id*: <dDQ5FD.A.-fC.RESNCB@poodle>*Resent-sender*: tesla-request@xxxxxxxxxx

Part 1

By Ampere, the inductance for a long air cored solenoid is: L = (u Nsqrd A) / h (where h is the length of the solenoid) (where A is Area ) (where N is the number of turns) Since: 2 pi r N = wire length*

*actual wire length = sqrt ( (2pirN)sqrd + (h)sqrd ) but we disregard (h)sqrd as an insignificant term.

Then: N = wire length / 2 pi r N

Substituting we get: L = u ( wire length)sqrd / 4 pi h

By Maxwell: u = 1 / Csqrd epsilon (Where C = 3x10 to 8 m/s)

Then: L = (wire length)sqrd / (epsilon Csqrd 4 pi h )

Part 2

For sake of simplicity in the following description of LC we will use the derived capacitance of an isolated sphere. This would be directly applicable to a Tesla coil secondary.

From Gauss: V = q/4 pi epsilon integral a to b for 1/ (r sqrd) dr

Since: q = cap Volt

Then: cap. = 4 pi epsilon (ab / b-a)

Since we have a single isolated plate, b approaches infinity we get: cap. = 4 pi epsilon R ( R is the radius of the sphere )

Now omega = 1/ sqrt (LC) Substituting and canceling we get:

1/ (omega sqrd) = (wire length / 3x10 to 8 m/s)sqrd x ( R/h )

So:

[omega = (C/ wire length) x sqrt(h/R)

*R must of course be decreased to accommodate the self capacitance of the coil.

Notice that the distance units cancelled for sqrt (h/R). Wire length and the speed of light provide the units for 1/s

END.

- Prev by Date:
**Re: Random TC Questions** - Next by Date:
**Re: Random TC Questions** - Previous by thread:
**Re: Random TC Questions** - Next by thread:
**Re: Wire length LC derivation,** - Index(es):