Can a toroid be used for a wah inductor?

[guitarleeman]

I was wondering if a toroid could be wound to 500mH,like an air core standard wah inductor coil. Also,do you have to always use really thin magnet wire to wind a standard 500mH inductor for a wah,or is there a math formula,etc that would allow you to use a few turns of thicker gauge magnet wire instead?

[R.G.]

I was wondering if a toroid could be wound to 500mH

Yes.

like an air core standard wah inductor coil.

standard wah inductors are not air core. They all have magnetic cores, usually ferrite.

Also,do you have to always use really thin magnet wire to wind a standard 500mH inductor for a wah,

Nope, you can use wire as thick as you like.

or is there a math formula,etc that would allow you to use a few turns of thicker gauge magnet wire instead?

There is no math formula that will let you use a few turns of thicker wire.

Here's the scoop. The inductance of a coil of wire of N turns is proportional to N squared. This is expressed as
L = k*N*N where L is the inductance, N is the number of turns, and k is everything else all balled up in one number you multiply by to get the number to come out right.

What's hidden inside k are things like the permittivity of free space, the physical form factors of the coil, and the relative permeability of the core material the coil is wound on .

The relative permeability of air is almost exactly that of a vacuum, which is 1.00000. What makes iron, nickel, cobalt, and certain ferritic oxides unique is that they have relative permeabilities that is bigger than one. Sometimes a lot bigger. For instance, many ferrites have relative permeabilities of 1000 to 3000. Good transformer irons (actually about 4% silicon steel alloy) can be upwards of 10-20 thousand. Weird alloys made for the purpose, like mu-metal can be even more.

What that means is that if you wind a coil on a wooden form and measure it, you get some inductance L. If you then slip an iron core inside it that's a perfect fit and measure the inductance, the inductance will be as much as several thousand times higher depending on how good a job you did in getting the core to fit without an air gap.

So you may freely make an inductor of any inductance you like by winding turns of wire. The thickness of the wire does not have any effect on the inductance, other than to force the physical size of the coil to be bigger and that affects the constant k. But when you put a magnetic core in, the inductance goes up. What you can't do is wind fewer turns and remove magnetic material. That's taking both things in the wrong direction.