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What is/are the thumb rules for determining an appropriate shape of an electromagnet? By appropriate I mean having a reasonable amount of attraction/repel strength towards metal pieces.

If I were to bend an existing electromagnet (made out of an iron core wound with appropriate wire) into, say, a heart shape, would it still function? Would different sections of it behave differently (distribution of poles across the heart shaped structure)?

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    \$\begingroup\$ What you are expecting from YOUR particular electromagnet: long strok, strong holding force, amperturn efficiency, less volume....what? As for the second question, the force remains the same but the magnetic lines will have a shorter return path and less lekage. \$\endgroup\$ – GR Tech Jan 19 '15 at 21:28
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A circular coil shape is the optimum use of wire to obtain the largest magnetic flux. Any deviation from a circle will use more wire for a given coil area and the extra coil resistance can reduce the peak current into the coil or, necessitate more power having to be delivered to the coil to obtain the same current.

There is a more subtle effect too. The magnetic field around the areas that form the V section in the heart will be significantly weaker because the wire will have to nip in and out sharply and the magnetic fields will tend to cancel at this point.

Having said all of that if you wind a circular coil and reshape the magnetic field into a heart shape by reshaping the iron this won't be such a problem.

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As long as you can get enough core behind the windings that the core does not saturate any shape of winding will work well. junk-yard crane elecromagnets are disk shaped cores with the winding in a circular groove. door electomagnets (maglocks) are bar shaped, with a double groove which holds the rectangular shaped winding.

The circular shape uses less copper to enclose the same cross-section of core which reduces the materials bill and/or by having lower resistance saves power.

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I sometime feel like a broken record. The force from a magnet will depend on the field gradient. One way to get a big gradient is to bend the two poles of the magnet so they are near each other. Where are the two poles in this video? Try winding a coil around an iron nail, and then bend the nail into "U" shape. Which holds a piece of iron with more force... (for a give coil current.)

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In a C shape(with the two points being the poles) your flux is at a maximum there, so although you won't get a good average but in the gap and pole points the magnet field will be very strong. The magnetic field will have less distance to travel and have a higher density in that area (flux)

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