Consider a toroidal solenoid powered by a sinusoidal voltage. This will lead to appearance of sourceless electric field, also sinusoidally varying with time. Now consider a conductive ball in the center of the system. Let the electric charge on the ball vary in phase with the voltage applied to the toroidal solenoid. Then there will be force acting on the ball, due to the E field, but no force acting on the solenoid - the net charge on the solenoid is zero, there are no sources of the field E produced by the solenoid. This violates Newton's third law (action and reaction). If you have thought about it earlier, please contact me at <personal email address removed>.