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I am stuck with a problem about voltages (electrostatic potential) and forces.

According to capacitor equations the energy stored in the capacitor is:

U=1/2*C*V^2

And force is:

F = - dU/dx

Since U is dependent on V^2, our force can’t be positive (repelling force)

Also if there is no voltage difference there will be no force

Am I wrong in any part of what I wrote above?

But let’s think about a gold-leaf electroscope (two very thin sheets of gold in a jar hanging on a conductive rod which comes outside of the jar). When we bring a charged object near the rod (I think we should also be able to do this with a battery too, right?) the two gold leaves repel each other. This makes sense if we think of electrons or protons repelling each other.

But if we think in terms of the equation above then the two gold leaves are at the same voltage and they should not exert any force on each other (and certainly not a repelling force because of the V^2 term in energy).

Another question can be: what will happen to two gold leaves at two different but both positive potentials (100V and 50V for example)?

A practical application of this problem is that people tell I can’t make an electrostatic actuator that has a repelling force (and I think they are wrong if we look at the electroscope example)

Could you help me with this problem? I am completely confused here :-)

Thanks in advance for your help

Dara