A cylindrical solenoid 10 cm long has 3000 turns of wire and carries a current of 5.0 A. A second solenoid, consisting of 2000 turns of wire and the same length as the first solenoid, surrounds it and is concentric (shares a common central axis) with it. The outer coil carries a current of 10 A in the same direction as the current in inner one.
(a) Find the magnetic field near their common center.
(b) What current in the second solenoid (magnitude and relative direction) would make the net field strength at the center twice that of the first solenoid alone?
(c) What current in the second solenoid (magnitude and relative direction) would result in zero net magnetic field near their common center?