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Registered Member #190
Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567
This is a theoretical and practical question:
Let's assume that one has a circular coil of many turns of copper magnetic wire. The coil has a hole in the middle, so there is an inside radius, r, and an outside radius, R. Now let a magnetic field cut through the coils so a voltage is induced. If the magnetic field is constant, is more voltage induced if the magnet is smaller, the same or larger than the hole? If the cost of wire is not an issue, but space is limited, would more voltage be induced if if we made "r" as small as possible to increase the number of turns, or will this contribute little to a voltage increase?
Registered Member #72
Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659
I assume you mean the magnetic field is constant with respect to the magnet, rather than constant in time? The latter, as Steve implies, won't make any voltage at all.
If you have a coil of copper (non?)magnetic wire, and have a magnetic field threading it, then suddenly change the field by whipping the magnet away, or by turning it round, then every bit of the wire is going to generate a voltage due to its flux linkage changing, and they are all going to be added up in series. This means you need to do an integration, ideally over the length of the wire, of the change in the magnetic field.
Failing that (no-one wants to do that), you take the mean radius and multiply by the mean field, and that probably won't be far wrong. Inituition about what geometry gives the best linkage for limited space can be off when you come to making the dimension ratios extreme, like going to very small r. The known gemeotry for best self-inductance given a known length of wire is to wind the wire into a coil of square cross section d x d, with a 2d diamter hole. This will not give the best result for every size of magnet, but is probably not far off if the size of the magnet is commemsurate with the size of the coil. Otherwise, get 3D integrating.
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Cutting a coil of wire with magnetic flux
