The way a motor works is fundamentally is it uses the force that the current carrying wire feels in a magnetic field to create a torque and make the coil spin.
Here is a picture of what a simple representation of that motor looks like:
The Magnet is placed on top of the battery. It doesn't actually matter if it interacts with the battery, in fact, it is used to create a magnetic field for the wire to feel force from. If you can imagine, the field lies in between the coil and the magnet.
The Current Carrying Wire is used because the electrons inside are moving around and feeling force from the magnetic field. This way, the coil can move.
The Coil is coiled and not just straight across because the reason it moves is by current running through the coils, so the more the current moves, the more the coil moves.
The way the motor actually moves is because the current carrying wire feels the force, yes. But you also have to encourage the spinning to direct the force in a circular way. The current carrying wire is coated so that you have to scrape off the coating on the parts you want to feel a force. For a spinning coil motor, you have to scrape the top of both sides. This means when your coil is facing you so that you can see through the loop, scrape the top of the wire on both sides of the coil. You can scrape the bottom as well as long as you're consistent.
We have to do this because the direction that the magnetic field goes is South to North, so the field lines run up. This is a picture Ms. Lawrence drew in her motor video which is very helpful!
I made one of these simple motors in class. Here is a video of it spinning/working:
Some uses of motors like this in a more complicated, sophisticated form are: In a car, or in a hairdryer or in a clock or in a robot.
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