Re; Inductance

Original poster: jdwarshui@xxxxxxxxx

Re: Inductance

For an air core solenoid:

 L = u Nsqrd Area / length

Or:

L = u Nsqrd pi (r)sqrd / length

Multiplying both numerator and denominator by 4pi we get:

L = u [ Nsqrd  4 (pi)sqrd  (r)sqrd ] / 4pi solenoid length

But:

[ Nsqrd 4 (pi)sqrd (r)sqrd] =  [2pi r N]sqrd = [wire length]sqrd

Then:

L =  u  [wire length]sqrd / 4pi  solenoid length

Now if we are interested in the total inductance of a straight wire we
can set the solenoid length to equal the wire length and we get:

L straight wire = u (wire length)/ 4pi

By Amperes law we can show that the internal inductance of a straight
wire is:

L internal straight wire =  u (wire length)/ 8pi
(this derivation is found in most electromagnetic textbooks)

Conclusion for the inductance of a straight wire:

Half of the inductance of a straight wire is internal to the wire and
half of the inductance is external to the wire.


Jared Dwarshuis