Suppose that you want to design a solenoid to control magnetically the central locking system of your car doors. This needs a magnetic induction at the end of the coil of 0.1 T. To be compact enough to fit next to the window winder mechanism, the coil can be only 2 cm long and 3 cm in diameter. The car battery can supply 4 A.
How many turns of wire does the coil need to have if it has air as its core?