I encountered this problem in a book, but there were no solution written there.
The setup: there is a plastic (insulator) circular disc, that is suspended in a way, that can very easily rotate (so the friction is negligible). On the disc, a coil is placed exactly around the axis of rotation. The ends of the coil are connected through a battery. The battery is assumed to be small in size. There is
I current flowing in the circuit. At the circumference of the disc, small metal spheres are placed at equal distances. These metal spheres are seperated from each other. Each sphere has the same electric charge
Q. The metal spheres are fixed to the place. (They can't roll away.)
Now, the disc is not in motion. The circuit is then broken.
The paradox: two outcomes are possible (but of course, only one could be right):
The magnetic flux decreases, an electric field is induced, that will exert a force on the spheres, torque is applied to the disc, the disc will rotate.
The angular momentum is conserved. The system had 0 angular momentum at the beginning, so it will have 0 later. The disc will not rotate.