Re: Faradays Law and Inductance

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Shaun Epp <scepp@xxxxxxx>

Ohhhhh  Noooooo..........  not that wire length thing again!!!!!


If you multiply the top and bottem by the same thing, you end up with 
one (1).  You could multiply the top and bottem with anything and 
make the equation say what you want.  Multipling top and bottem by 4 
pi  does not prove that wire length has anything to do with this the equation.

Shaun Epp


----- Original Message ----- From: "Tesla list" <tesla@xxxxxxxxxx>
To: <tesla@xxxxxxxxxx>
Sent: Tuesday, October 31, 2006 11:08 AM
Subject: Faradays Law and Inductance


> Original poster: "Jared Dwarshuis" <jdwarshuis@xxxxxxxxx>
>
>
> Faradays Law and Inductance:
>
>
>
> For an air cored solenoid:
>
>
>
> Closed integral E dot ds =  d (flux B)/dt
>
>
>
> Closed integral E dot ds =  (Area)   d(B)/dt
>
>
>
> Closed integral E dot ds =  (pi  r(sqrd) )   d(B)/dt
>
>
>
> Using B for a solenoid from Amperes law:
>
>
>
> B = u   Ienclosed / height of solenoid
>
>
>
> We get:
>
>
>
> Closed integral E dot ds  =  u (pi  r(sqrd) ) / h          d( Ienclosed)/ dt
>
>
>
> Multiplying numerator and denominator by 4 pi we get:
>
>
>
> Closed integral E dot ds  =  u (2pi  r)sqrd / 4 pi h     d (Ienclosed) /dt
>
>
>
> Since:  Ienclosed = (N)  Io          ( Io is the current in a given turn)
>
>
>
> Closed integral E dot ds  = u (2pi r)sqrd / 4 pi h      ( (N)   d (Io)/dt )
>
>
>
> Since:
>
>
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> u = 1 / e Csqrd      from:  1/ sqrt( u e ) = C
>
>
>
> We can equivalently write:
>
>
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> Closed integral E dot ds  =
>
>
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> 1/( 4 pi  e h)     (circumference/ the speed of light) sqrd       ( 
> (N) d (Io)/dt )
>
>
>
> Since: Voltage = (N)  d (flux B)/dt
>
>
>
> Then:
>
>
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> V =   [u (2pir)sqrd (N)sqrd /4pi h]   d(Io)/dt
>
>
>
> Of course:  (2pi r)sqrd (N)sqrd = (2 pi r N)sqrd
>
>
>
> And since (2 pi r N) is the physical wire length of the solenoid:
>
>
>
> V =   u (wire length)sqrd / 4pi h         d(Io)/dt
>
>
>
> Or:
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>
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> V = (wire length/ speed of light)sqrd       1/ (4pi e h)       d(Io)/dt
>
>
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> Both forms are identical to:
>
>
>
> V = L d(Io)/dt
>
>
>
> Observations:
>
>
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> We have acquired a factor of (N) from the law: V = (N)  d(flux B)/dt
>
>   (This part demonstrates how each loop contributes voltage).
>
>
>
>  We acquired a second (N) from the current component of the equation:
>
>  Ienclosed  = Io (N)
>
>
>
> Since:
>
>
>
>  [(2pi  r)sqrd ] [Nsqrd] = (2pi r N)sqrd = (wire length)sqrd.  We 
> can clearly see that wire length is a fundamental geometry for 
> describing air cored solenoid inductance in the framework of 
> Maxwell's equations.
>
>
>
> ( Interestingly; in the second form for voltage, we  find an inverse 
> capacitance in the form: 1/ (4pi e h). This strongly suggests that a 
> shell theorem for solenoids may exist. )
>
>
>
> Sincerely: Jared Dwarshuis, Larry Morris      Oct. 2006