|MadSci Network: Physics|
Dear Nikos David and I are very interested in your questions. The arrangement you describe with Helmholtz coils is contrived to give UNIFORM H field at that mid-point where you have placed the current carrying wire. The force on the wire is OF COURSE the same force as that on the coils (half each). If you assumed anything else you'd have a perpetual motion machine - a self mover by pulling up on its own shoe-laces! Most tasks have an EASY way and a HARD way. You chose a HARD way - calculating the force on a CIRCULAR coil. A much BETTER idea would have been to PRETEND it could not be much different to that of a SQUARE coil - for that is easy to calculate (as the force between a wire and 4 parallel wires! Nevertheless you calculated it for round coils. Well done! You found a force of attraction and an equal force of repulsion. Well done! You then made a fatal error! Look at it this way: If you are pushed NE with force F and pulled SE with the SAME_strength force, which way do you go? (Vectors only cancel if in the SAME direction! (and if one a push the other a pull) And of course the EASY way is the force is simply Bi at each unit length of the wire. Of course B varies in magnitude along the length of the wire and is not zero anywhere, but you will get ROUGHLY the right answer if you assume B is const over all the length of wire of length D = diam of Helmholtz coil. Why not set up a spring balance ( or counterweight balance) and DISCOVER it for yourself. Much more fun than asking "experts"! A curtain rod and string would make an EXCELLENT balance. Have lotsa fun John and David
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