Electrostatic force, voltage, electrostatic potential

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SUMMARY

The discussion centers on the relationship between electrostatic potential, voltage, and force, specifically in the context of capacitors and electroscopes. The energy stored in a capacitor is defined by the equation U=1/2*C*V^2, while the force is derived from the change in energy with respect to distance, F = -dU/dx. A key point raised is the confusion regarding the repelling forces observed in a gold-leaf electroscope, which appears contradictory to the equations governing electrostatic potential. The conversation clarifies that the force can indeed be positive if the change in potential energy is negative, emphasizing the importance of understanding electric fields and potentials in electrostatics.

PREREQUISITES
  • Understanding of capacitor equations, specifically U=1/2*C*V^2
  • Knowledge of electrostatic force calculations, including F = -dU/dx
  • Familiarity with electric fields and their relation to charge and potential
  • Basic concepts of electrostatic potential and voltage
NEXT STEPS
  • Study the relationship between electric fields and forces using F = q*E
  • Explore the concept of electric potential and its units in detail
  • Investigate the behavior of charged objects in electrostatic systems
  • Learn about practical applications of electrostatic actuators and their design considerations
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Students and professionals in physics, electrical engineering, and anyone interested in the principles of electrostatics and their applications in devices like capacitors and electroscopes.

dara bayat
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Hello everyone

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
 
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apparently my question is too stupid :)

or did I post it in the wrong category?
 
dara bayat said:
Hello everyone

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
..

Hmm, I can't follow. Above, the energy U is not a function of distance x.
The force on a probe charge in electrostatics is usually

F = q*E = -q*dU/dx

with E(x) for the electric field, q for the charge of the test object and U(x) for the ELECTRIC POTENTIAL (same units as VOLTAGE, not energy). I guess that you have confused something!?
 
Why can't the force be positive? If the change in U is negative, then the force will be positive, right?
 

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