# Interesting geometric problem with circles

1. May 5, 2007

### Jdo300

Hello All,

I'm thinking of an interesting geometric problem with circles and I'm wondering if there is a way to calculate the following:

Lets say I have a bundle of wire that I use to make a Helmholtz coil. These coils will have a circular cross-section like circular rings here:

http://www.daedalon.com/em.l.jpg

I'm trying to figure out what gauge wire I want to use to wind the coils with but I want to see if I can calculate the cross-sectional diameter of the bundle of wires that would make up the coil.

So, If I look at the wires as being a bunch of little circles inside a big one, is there a way to geometrically determine what the diameter of the large circle would be with X number of smaller circles each having diameter D?

I thought about simply taking the area of each small circle and equating that to an equivalent large one, but that would be cheating since there would be gaps between the smaller circles.

Thanks,
Jason O