Perpetual motion machine I'm having trouble understanding why this machine doesn't work. Part of a ring, half of which is uniformly charged, is located between two oppositely charged plates, attracting to the negative one and pushing away from the positive one, thus gaining angular momentum. 
I understand that perpetuum mobile is impossible, however, I'm interested why in terms of electrostatics and mechanics this machine can't accelerate infinitely.     

 A: Perhaps a gravitational analogy will help?
The positive charges are railway trucks on a circular track in a frictionless environment.
The positive plate is the top of a hill and the negative plate is the bottom of the hill.  
Set the railway trucks moving
The trucks going down the hill lose gravitational potential energy whilst there are trucks going up the hill gaining the same amount of gravitational energy.  
So in theory the trucks can remain in motion for ever but no energy can be extracted because that will slow down or stop the trucks.
And there is also friction to consider.
A: I have reconstructed your diagram  computationally and numerically computed the potential energy as a function of the orientation of the ring:

As you can see, when we neglect friction (something that you can't do in the real world) the machine is indeed capable of perpetual motion. However, some important points:


*

*The total change in energy of the system per revolution is zero, so if you attempt to extract energy (or friction acts) then the device will grind to a halt. This is independent of how large you make the E-field.

*In order for the system to complete a revolution, you need to put in the requisite energy. Either by starting the system at the peak of the potential energy, or giving it sufficient kinetic energy to overcome the peaks. You might as well remove the charges entirely and just spin a wheel.

*You may wonder whether dynamically adjusting the E-field in order to increase the acceleration-stage and attenuate the deceleration-stage would allow you to overcome friction/extract energy; if you do the calculation you will find that it takes as much energy to dynamically adjust the E-field as you get out of it.

