Solenoid and charged disk 
If we put current on the solenoid, it makes change of B field.
Then I think charged disk will rotate, but I don't know where the angular momentum came from.
 A: The total angular momentum of the whole system remains at zero, because the field itself contains angular momentum which exactly cancels out the angular momentum of the charged disk. 
How do we know this? Suppose that you switch on the current and then you slow the disk to a stop, so there is no mechanical angular momentum. Then switch off the current, causing a changing magnetic field $\to$ a non-conservative electric field with nonzero circulation around the disk $\to$ a nonzero torque on the charged disk. The disk will then rotate, in the opposite direction that it did beforehand. Where did its angular momentum come from? From the field - there's no other place for it to come from.
More formally, if a charged mechanical system interacts with the electromagnetic field, then none of the usual conservation laws - of energy, linear momentum, angular momentum, and centre of energy - is guaranteed, because you're interacting with either an external system or internally with nonconservative forces. However, it is possible to formulate global conservation laws for the entire system, which include energy and momentum terms for the fields themselves as well as power/force/torque terms for the transfer of the conserved quantities, that do give conservation of these quantities for the entire system. It is only in this sense that angular momentum is conserved.
