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:

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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.
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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.