In physics class we have to do some experiment dealing with electricity and magnetism. I wanted to do something easy, but I asked a question in class that led my professor to believe I wanted to find the optimum diameter for a ring launched in a Thompson coil.
What a Thompson coil does is runs alternating current through a coil, crating a magnetic field. When you place a metal ring around the coil, the magnetic field induces a magnet in the ring which creates a force on the ring to launch upwards. Like this

My problem is that a magnetic field produced by a ring looks kinda like this. Where the force produced on the ring is directed at 90° angles to the magnetic field lines.
Due to this directional property, it would make sense that a ring that is large would have a greater portion of the force would point in the direction of acceleration, because where magnetic field lines are horizontal, all force due to the magnet points up.
However, the larger a ring gets, the less force is felt by the magnet, due to it simply being farther away.
My task is to find the ideal diameter for ring to be in order to produce maximum force in the upwards direction.

Yikes, I'm probably going to ask a bunch of TA's.

It's got something to do with trying to make F=iLxB and an integral in the form μi/2r. And finding the maximum values when they are equal. I think...

Post has been edited 1 time(s), last time on Apr 1 2008, 6:53 am by Rantent.

Rantent I'm not exactly sure what you're asking us to do. If you're looking for an ideal diameter of a ring, you're going to have to take into account the Magnetic forces, fields, velocity of the charge, currents and charges induced, etc. Not to mention the outer and inner diameters of the ring.

But neways, try some of these equations:
Magnetic force: F = iLxB -> qvxB
B = μ*I/(2*pi*r) Axis of Loop: B = μ*a^2*I/(2(a^2+x^2)^(3/2))
Circular motion: F = mv^2/r = qvB T = 1/f = 2*pi*r/v
Lorentz force: F = qE + qvxB
Hall effect: V = Fd/q, U = -μ*B
Biot-Savart Law: B = μ*I/(4*pi*r^2)∫ds

YAY! Thanks for posting that, I needed the Biot-Savart Law, I think.

And yes, that is exactly what I'm doing, finding an equation that relates the size and current in the Thompson Coil to a maximum applicable force for a ring.
While assuming that there are no external fields or resistances, ect. and everything is ideal.

Np. I actually just learned this shit like a couple weeks ago. We've been given a cheatsheet with all the equations we'll ever need for physics when it comes to electricity, magnetism, or optics. Here's my present for ya:
[attach=799]
see if it works

Attachments:

Dear Rantent:
Easy stuff is great if you're just trying to squeek by and get on with life. Yet in the greater scheme of things, by not challenging yourself, you actually do yourself a disservice. Train your brain now, while it's still young and developing. It's not the projects or the tests that matter, not their content specifically, but merely the act of rising to the occassion that helps you in the long run. Not meaning to sound preachy, but time goes by damn fast as you age, and it doesn't slow down. The older you get, the harder it is to develope and maintain healthy habits.

Keep your brain activity up by constantly learning new skills and knowledge, which helps keep your brain healthy and in peak shape (that, along with bloodflow and good nutrition), not unlike working out at a gym on your muscles or performing aerobic exercise for your cardiovascular system. (Actually, on that note, exercise is great for said bloodflow, whereas smoking, alcohol, and too much caffine reduce bloodflow)

Anywho, physics is not my area of expertise, so I wish you luck! =o)

You make a good point, but I don't really consider the topic of finding an ideal diameter for a ring used in a Thompson coil to be relevant. Where as the "easy" topic I had decided on would be much more useful to me. I didn't explain what my original idea was, to focus on the topic at hand, but I wanted to find the minimum voltage that would electrolyze water, while varying the salinity in a solution. This is much easier in terms of accessible theoretical data, as well as comparative results. Finding the diameter of a ring and comparing that with experimental data is much more difficult. (Because I have to build both a Thompson coil and various aluminum rings.)

A simple experiment designed for a more useful purpose is more intriguing to me than a complex one to verify a rather inconsequential theory.
Making hydrogen from water is rather exciting, and is becoming an increasingly important reaction, while the ideal size to induction ratio for a ring around a coiled wire is rather.. Obscure.

It might help if I were to be going into a field of electric train research or building rail guns, but going into chemistry, I really wanted to do something with electrolysis.

Dear Rantent:
I gotcha. Did you try to explain these views to the teacher after class? I'm sure he/she/it/floating head would have been willing to change your assignment after understanding your passion and goals.

On a sidenote, what in the world is up with that "Reported" banner above my post? Did someone accidentally click it, or do I have a secret admirer? Oh boy! =oD