What is $L$ for a ring Electromagnet? I am looking at the force equation for an electromagnet from Wikipedia (https://en.wikipedia.org/wiki/Electromagnet):
$$F=\frac{\mu^2N^2I^2A}{2\mu_0L^2}.$$
I'm not sure what $L$ is. It seems like this would be the length of a bar (specifically of the core of the bar) if $I$ was making a bar electromagnet. I want to make a ring electromagnet, though.
The inner diameter will be 9 inches and the outer diameter will be 10 inches. Is the length just the difference in radius (10-9=1 inch) ?
Any help is greatly appreciated! Thanks!
I basically just want an approximate value.
Someone commented that the flux path is average circumference. Wouldn't that be:
$2*\pi*(10$ inch $-9$ inch$)=0.15959$ meters ?
Say I'm using iron (mu is .25), 500 turns, 1 Amp (which I know is a lot), and area is 0.04 m^2 (from radius values). If I just assume L is .15959, the force is huge. Doesn't make sense.
$\frac{(.25^2*500^2*1^2*.04)}{(2*0.000001256637061*.15959^2)}=9.764 × 10^9$ Newtons? 
Here is a picture of what I mean (The pink area is where I'd like to find the force):

 A: Equation Analysis
$L$ comes from the equation of a magnetic field produced from a solenoid:
$$B=μnI$$
where $I$ is the current, $μ$ is the magnetic permeability of the material through which the magnetic field is forming, and $n$ is the number of turns per length of wire $n=N/L$
However, what you are using isn't a solenoid it is a toroid, thus you need to use a different equation.
The magnetic field produced by a toroid, $B$, is (Note the similarity between magnetic field produced by toroid and solenoid):
$$B=μNI/{2πr}$$
Where $r$ is the midpoint radius between the outter radius and the inner radius as shown by this picture:

Calculation with given parameters


*

*Magnetic Field of Toroid


Given:
$I= 1 A$, $N= 500Turns $ , $μ=0.25 , $r=9.5 inches= 0.2413 meters$
$$B={0.25)(500)(1)}/{(2)(π)(0.2413)}$$
$$B=82.446 T$$
However, note that the magnetic field only exists inside the toroid's core itself which could be verified by ampere's law thus you wouldn't be able to use it to impose an effective magnetic force on any external system


*Force on required shaded area



Thus $B$ in shaded area is zero and $Fb=0$
