Could a Lorentz engine (like the ones that move the write head inside of hardrives) be used to run car ? Would it be possable to get it producing 60hp, and a decent amount of tourque, if so how large would it have to be / what would its power consumption be ?
Every electric motor runs using the Lorentz force, so there is no difference in principle between the motor in the hard drive and an electric car motor. There are commercial 60 hp electric motors that run electric cars, so the answer is yes. It's power consumption is, well, 60 hp. That's 45000 watts, plus a little more for heating the engine and so on, so say an even 50,000 watts. This randomly selected 60hp electric motor is about 18 inches across: (look for 364T in this link).
Yes, such an engine would be possible. For a circular motion you would need to modify the setup a little bit but not significantly.
While Ron is absolutely right that there is no difference in principle a big engineering/economical problem is that an engine with such a design would need very large and powerful permanent magnets. NdFeB magnets in a size enough to create 50kW would be quite heavy and expensive.
A standard electrical motor such as the one shown below from a vacuum cleaner does not require a large amount of rare earth materials. Instead all fields are created by coils wound around a high permeability material (iron alloys or for high end motors alloys with some amount of Nd).