Electrostatic force, voltage, electrostatic potential

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Discussion Overview

The discussion revolves around the concepts of electrostatic force, voltage, and electrostatic potential, particularly in the context of capacitors and electroscopes. Participants explore the relationships between energy, force, and voltage, as well as practical implications for electrostatic actuators.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the equation for energy stored in a capacitor and suggests that since energy is dependent on voltage squared, the force cannot be positive, leading to confusion about the behavior of an electroscope.
  • Another participant questions the initial claim by stating that the energy U is not a function of distance x and clarifies the force equation in electrostatics, indicating a potential misunderstanding of the terms involved.
  • A different participant challenges the assertion that force cannot be positive, suggesting that a negative change in energy would result in a positive force.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between energy, force, and voltage, with no consensus reached on the implications for electrostatic forces in the context of the electroscope example.

Contextual Notes

There are unresolved assumptions regarding the definitions of energy, force, and potential, as well as the applicability of the equations presented in different scenarios.

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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