Why do we need a coil to make a magnetic field?

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Why do electromagnets always need a coil to generate a magnetic field, and why do you need a AC current to generate inductance?

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tl;dr, any electricity flowing makes magnetic fields, coils make usefully shaped magnetic fields.

Electricity flowing in a straight line causes magnetic fields in circles curling around the line, kind of like saturn’s rings orbiting the wire. This is a fundamental physical relationship between electricity and magnetism. Change in one causes an amount of the other in a perpendicular way.

If you make a coil of wire, each tiny piece of the coil looks like a line if you zoom in far enough, which makes its own tiny ring of magnetic field around it. Because they’re facing different directions, if you add all of them together, most of the perpendicular parts cancel out with others in the opposite direction, but on the inside of the ring they’re facing the same direction and add together. So the total net magnetic force is a straight line following the inside of the coil. Which is useful for pushing things.

A DC current will just push in the same direction forever. This is useful if you have something like a railgun where you want to launch something in that direction and have it never come back. This is less useful if you have a motor that you want to move back and forth or in circles or something. A DC current is going to push it as far as it can in one direction and then it’ll get stuck when it goes as far as it can in whatever contraption you’ve built. An AC current cycles back and forth, back and forth, which is useful if you want to move your motor back and forth and then use that to turn a wheel or move a car or something.

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