Coilgun or Railgun?
P.S. I've found places on the internet that give tutorials on making capacitors, which I would also consider doing. If I'm able to make large-capacity capacitors myself and use those, should I build something other than what I should make if I only have access to camera flash capacitors?
P.P.S. I heard the following rule somewhere here on this site: "The more amps in a coil, the more powerful its magnetic field, the more voltage in a coil, the larger the magnetic field." Is this true?
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Answer it!
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If you are using normal conducting wire, then the voltage you use determines the current. The two are not independent, they are simply proportional (homework problem: why is that statement true, and who said so first?).
A magnetic field falls off as a power of distance (1/r3 for a dipole), so a field which is "more powerful" at a given distance will also appear "larger", in the sense of having the same strength as the weaker field but at a farther distance from the source.
If you want to use a single capacitor with a very high storage capacity, you would be better off purchasing or scrounging one (from a car audio system, an old CRT, or something) than trying to make it yourself. The problem is defects in the materials you use (small holes in your dielectric, for example) will either reduce the final capacitance, or make the device nonfunctional.
The shape of the field -- how far it extends in any direction (for a fixed fall-off in stretch), the angular dependence of the field -- depends only on the geometry of the system. By "geometry," I mean way the coils are wound, their shape and their spacing, and the core you have them wound around. The electrical configuration does not (cannot!) affect the field shape.
The strength of the field -- how much force it exerts at a particular location -- does depend on the electrical configuration, but that dependence is simple. The more current you run through the wire, the stronger the field. That's it. You can express that same dependence in terms of the voltage applied (there's that homework problem again), but you won't get a different answer.
The capacitors supply current (or voltage, if you want), and how much current they supply depends on how you configure them. Parallel vs. series will make a difference (more current faster, or less current for a longer time), and that difference in current will affect the field strength, as I've outlined above.
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