Yes, you can charge a car that way, but it is actually more inefficient to do so.

Basically, if you try to create electricity using "electromagnetic induction", it requires more energy. You can feel this for yourself if you ever try to charge anything by cranking on a reverse-motor (basically it generates electricity from motion, instead of generating motion from electricity. All the motors in your car, vacuum cleaner, almost anything with moving parts do this). These reverse motors are actually just the coil and wire and a magnetic field, which is the situation you're thinking about. If you connect something to power using a reverse motor, you will see it becomes harder to turn the crank. You can't get free energy!

And so you need even more electricity to accelerate your wheels, and your car slows down faster. And since the method of using this is not 100% efficient, you actually lose energy overall. Basically you're using electricity to run a motor to turn some wheels to run a reverse motor (which takes even more energy to run).

However, you may have heard that the brakes charge the car back up in hybrid cars. And that is what they do: they take advantage of the fact that generating electricity by this method slows your car down more, and they use that to help charge the batteries in hybrids while at the same time using it to help slow down your car.

No, but not because what you have learned about magnets is wrong - far from it.

A changing magnetic field - which includes a magnetic field of a moving source, such as a moving magnet - generates an electrical field. This *alone* generates the electric field; the only purpose of the coil is that the electric field will generate no electricity if there is no electrical conductor upon which it can work.

The problem that you are running into is the Second Law of Thermodynamics - that disorder, "entropy", always increases, and you can't recycle spent energy. Now, you could do what you are suggesting, but the car's battery would run down faster than the magnet would charge it back up again. You have a diminishing returns problem. Moreover, the generation of the electrical current that recharges the battery generates its own magnetic field, which counteracts the movement of your magnet, and whatever it is attached to by extension. This would mean that not only would your system not allow your car to run indefinitely, it would also make your engine work harder to go a certain speed, running the battery down even faster. And, because the transfer of electricity to recharge the battery isn't perfect either, some energy being lost to become heat, this means that you would actually make the car *less* efficient than what you started with.

However, here is something that you *could* do: have magnets that clamp on or electromagnets that activate when you actually want to slow the car down, i.e. you hit the brakes. This would not make the car any more efficient just driving, but it would make the car much more efficient when stopping and starting again at stoplights, turning, etc.