--- For a solenoid, its internal magnetic field is described by:
µ N I B = ------- l where µ is the permeability of the core, N is the number of turns surrounding the core, I is the current in the coil, and l is the lenghth of the coreso, you can see that B will increase if the permeability of the core increases, the number of turns increases, the current increases, or the length of the core decreases.
To get the maximum strength, then, you want to wind a short solenoid with a lot of low resistance wire because, as the resistance increases the current will decrease for a given supply voltage.
Also, you'd like the external field to add to the internal field, so you'd want the solenoid to be encased by a high-permeabilty core.
To do that you'd want the core to be shaped like a bundt cake pan, with the coil nested inside of it, like this side view: (View in Courier)
. +---+ +---+ +---+ . | |ooooooooo| |ooooooooo| | . | |ooooooooo| |ooooooooo| | . | |ooooooooo| |ooooooooo| | . | |ooooooooo| |ooooooooo| | . | +---------+ +---------+ | . | | . +-------------------------------+
That way, the part of the magnetic field which would be lost will be captured in the walls of the "core" and will add to the pull of the center leg.
That's how junkyard electromagnets are made, BTW.
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--- Both lengths _don't_ cancel out since one is the length of the wire used to wind the coil and the other is the length of the wound solenoid.
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--- In a sense, yes, but you also need to be concerned with how many turn of wire you can get on the thing because that, and the current in the coil (ampere - turns) will determine the strength of the magnet.
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--- Not necessarily.
If you want to get a feel for the numbers, here ya go:
Let's say we have a core that looks like this:
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