This is a famous paradox, from the Feynman lectures.
It goes as follows.
There is a very long solenoid which has a current flowing in it and so there is a magnetic field inside(and outside if you wish) the solenoid. In addition the solenoid is surrounded by a number of charged balls placed on a disk.
The paradox is as follows:
If the circuit is now broken the Magnetic field will drop to zero, and so an electric field will arise which will tend o make the balls rotate. Thus when the dust has settled the balls will be rotating and the system will have angular momentum. Where did this angular momentum come from.
The solution to the paradox lies in the fact that initially there is both an electric field and a magnetic field in space. Crossed electric and magnetic fields have angular momentum, and thus the system does have angular momentum even initially.