Conservation of energy gone for a six?

[manjuvenamma]

Let us charge a capacitor and disconnect it from the battery. Let the capacitance, charge and voltage of the capacitor be C, Q and V respectively. Now do some work and reduce the distance of the plates of the capacitor and make it half of the original distance. What are the energies stored in the capacitor before and after the reduction of distance? The energies can be calculated as square(Q)/2C and square(Q)/4C respectively. Where has the energy gone from the capacitor?

 

[Doc Al]

The energy was dissipated by whatever brought the plates together. Note that the plates are oppositely charged, thus one must do negative work to bring the plates together.

A similar situation can be had with gravity by lowering an object. The energy decreases. Where did it go?

 

[manjuvenamma]

You must be right. But I think I am missing a point.
Whien a stone is raised to a point, it has potential energy. If leave it there, it comes down.
If charge a capacitor, leave the plates as they are, they don't come closer on their own. Does the system do any work to bring the plates closer, or an external agency shoud do work?
Sorry, for the basic nature of my question. But I can't help asking, to convince myself.

 

[Dale]

If charge a capacitor, leave the plates as they are, they don't come closer on their own.

Think about this more carefully in the context of your question. What does Coulomb's law suggest about the force between the plates?

 

[D H]

You must be right. But I think I am missing a point.
Whien a stone is raised to a point, it has potential energy. If leave it there, it comes down.
If charge a capacitor, leave the plates as they are, they don't come closer on their own.

The plates don't come closer on their own because something (nonconducting spacers or some other physical constraint) is preventing that from happening. The exact same situation applies to the rock. Tie a rock to a rope, suspend the rock via a pulley, and tie the free end of the rope to some anchor. Voila, the rock is suspended above the ground with some energy proportional to the height of the rock. Now untie the rope from the anchor, lower the rock halfway to the ground, and retie the rope to the anchor. Has conservation of energy taken a six here? Of course not. You let the rock do work.

Back to the original problem. Just as the rope is needed to keep the rock from falling to the ground, some agent is needed to keep the plates of the capacitor apart. Suppose that agent is a number of nonconducting Hookean springs. Removing half of the springs will half the distance between the plates. Where did the energy go? You took it away by removing the springs.

 

[manjuvenamma]

Great, thanks, my mind is clear now. I understand it now.