Hire a Physicist

There are a lot of engineering conslulting services - fewer physicists.

What kind of physicist do you need? A solid state physicist is different from a condensed matter is different from astro from nuclear, etc.

Consultants I know go from $100 - $500 per hour.

 

Careful.

 

You've got an uphill climb.

Folks who do theoretical physics as a hobby have something of a bad reputation among physicists with PhDs.

You could try starting a discussion on the Physics Stack Exchange: http://physics.stackexchange.com/

But short of going to grad school in Physics, I'm not sure I can recommend many paths with confidence that will accomplish what you want to do.

You could also try visiting the Physics Depts of nearby universities, but you are going to need a quick pitch to convince hearers that you are not a crank wasting their time.

If your budget is only a few hundred dollars, odds are you will only interest grad students, and then you have the challenge of finding one who can really contribute to your problem on that budget.

To interest PhDs, you probably need to catch their attention very quickly with a brilliant idea, or bring a lot of cash to the table - in which case you are more of a grant source than collaborator. Physicists are not accustomed to the funding source also being the collaborator.