# Re: New Inductance Formula

```Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>

Tesla list wrote:
>
> Original poster: "David Thomson by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <dave-at-volantis-dot-org>
>
> Hi Antonio,
>
> >The inductance of a long solenoid is given, theoretically, by:
> eq1 >L=u0*a*N^2/l H
>
> Where did you find this formula?

This is sort of the fundamental definition of inductance of a coil... from
first principles. You'll find it in any first year physics text.

It is interesting in that it uses metric
> units and gives inductance as henry.

Not surprising, since mu0 (u0)(permeability of free space) is part of the
defintion of SI that hangs all the units together, along with epsilon0
(permittivity of free space), which in turn are tied to the velocity of light.

The values are not very accurate, but
> it can be modified to give better results.
>
> eq2 >L=4*pi^2*2.54/100*r^2*N^2/(10*l+9*r) uH

This is just a Wheeler type approximation to take into account end effects
on a real solenoid (and to convert from inches to meters)

Wheeler isn't derived from first principles, so I'm not sure dimensional
analysis is appropriate.  It's an engineering approximation with
(obviously) rounded coefficients.  I'd be truly amazed that ANY basic
equation has nice integer coefficients like 10 and 9.  No... nature is more
like 3.1415926535... and 2.71828.... and

```