Update: Sorry, I misread one of the symbols. The conclusion is that the force is L*(I cross B) where L is the length of the wire segment, I is the current vector and B is the magnetic field vector.

The assumption is that the magnetic field is constant over the length of the wire segment.

I couldn't find an online example worked out, surprisingly.

Most of the stuff in the wiki article isn't needed for your case. What you need is the expression for the force on a current carrying wire: F = I (L X B). F is the force, I is the current. L is a vector with magnitude equal to the length of the wire, and its direction is the direction of the current flow. B is the magnetic field vector. All of this assumes a constant field along the wire and a straight wire.

That's likely not the case, so you have to go to infinitesimal wire segements and integrate: dF = I (dL x B).

I don't know if this has made it any clearer for you, I'm assuming from your post history that you have done stuff with vectors/numerical integration before and just needed the bullpucky separated from the stuff you need in the wiki article. If it hasn't helped, I wouldn't mind doing an example in Perl tonight/tomorrow evening if nobody else has.

Edit: How is your model of the situation stored? I assume you've got a function that, given x,y,z, gives you the magnetic field vector at that point, but what of the wire?

It's going to be used in a OpenGL simulation written in Perl.

Maybe this is something? em_uniform1d.cpp Be sure to check the documentation link on the page as well.

Hope this helps.

Update:
I have decompiled a Java applet (guess that makes me a sinner?!) but the code s*ck*d.

Free Maxwell book with real solved problems See Chapter4 Problems for straight wire.

Maxwell Answers Search for Oersted on that page.

The big problem as I see it, is what are the assumptions made to simplify calculations. For instance, do you assume a uniform temperature always( affects resistance)? Another simplification would be assuming the wire has 0 radius, otherwise you need to account for different current flow at the skin versus the center. You might want to ask in the newsgroup sci.physics.

If you wanted some real world examples, I would also look at Electrical Engineering sites for examples of power line computations. I'm sure somewhere, some EE has a rule of thumb calculation for the Force on his power lines, especially at substations where short connections are made at high power. Maybe there is a Schaum's Outline Guide for Electrical Engineering, which contains simplified calculations and solutions for common problems?

It depends how accurate you want your simulation to be, how confident you are with vector calculus and numerical integration.

The force on a wire carrying an electrical current can be approximated by F=BIL where, B is the magnetic flux density the conductor is exposed to, I is the current running through the wire and L is the length of the conductor.

This is a highly simplified equation which can be taken as an upper bound on the numbers you should achieve partly because it relies on an infinitely long conductor.

The numerical simulation of time varying electrodynamic problems is not trivial. For example, time stepping requires good guesses of skin depth to be able to achieve any accuracy.

This may be of interest just to get the numbers out.

This rail gun intro might be helpful to you. At least the math is comprehensible.

Rather than reply to every post individually, this is a collective thanks to everyone who replied. I have more than enough reading to keep me going for a while, along with a bunch of equations I understand, and some worked examples to give me a feel for the values involved. I couldn't have asked for more. My faith in the collective wisdom of this place is reconfirmed.