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Feb18-13, 01:42 PM
Sci Advisor
PF Gold
P: 2,063
Well, I'm afraid that you messed up virtually every principle and aspect of magnet design.

1. 220,000 turns, at a 2.6" geometric mean diameter, corresponds to over 150k feet or 30 miles of 24 gauge wire. Can you could get a single spool or are you going to create joints?

2. The resistance of this coil is 3900 ohms which implies a 1950 V potential across the coil. This is far (really really far) above the insulation breakdown voltage for magnet wire.

3. The power dissipated is approximately 1 kW, which would quickly melt your coil (except for the fact that it would arc over first).

4. Your turns calculation did not include the thickness of insulation, the finite ability to pack wires tightly, or room for cooling tubes and potting compound.

5. The formula for the field inside a long thin solenoid is [tex]B=\frac{\mu_{rel}\mu_0NI}{length}.[/tex] Even this formula, however, does not apply to a very thick solenoid such as you have specified.

6. You messed up the units. The formula above is correct for SI units (mks, and tesla).

7. Special alloys like moly-permalloy have a relative mu of close to 1 million, but are completely useless for this application due to their incredibly low saturation field. You'll need to use iron.

8. Iron saturates at the relatively high value of 10 Oe applied field, which is still quite low. At which point its effective permeability approaches 1. The art in magnet design is balancing iron and windings so that most of the iron remains unsaturated.

In short, the magnet that you propose is unworkable and the field that you calculated is seriously in error.