Electrostatic force, voltage, electrostatic potential

In summary: If there is no voltage difference there will be no force. But if we have a voltage difference, then the potential difference will cause a force.This problem is confusing me, so could you help me out? Thanks!
  • #1
dara bayat
8
0
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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  • #2
apparently my question is too stupid :)

or did I post it in the wrong category?
 
  • #3
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!?
 
  • #4
Why can't the force be positive? If the change in U is negative, then the force will be positive, right?
 
  • #5
,

Hello Dara,

You are correct in your understanding of the relationship between voltage, electrostatic potential, and force. The equation for energy stored in a capacitor, U=1/2*C*V^2, shows that the energy is directly proportional to the square of the voltage. This means that an increase in voltage will result in a larger amount of energy stored in the capacitor. Similarly, the force between two objects is also dependent on the energy, as shown in the equation F = - dU/dx. This means that the force between two objects is also dependent on the square of the voltage difference between them.

In the case of the gold-leaf electroscope, the two gold leaves are at the same voltage because they are connected by a conductive rod. However, when a charged object is brought near the rod, it creates a voltage difference between the two leaves. This voltage difference results in a force between the leaves, causing them to repel each other. This force is due to the electrostatic potential difference created by the charged object.

In the case of two gold leaves at different positive potentials (100V and 50V), there will be a force between them due to the difference in their electrostatic potentials. The higher potential (100V) will have a larger force, causing the leaves to repel each other. This is because the energy stored in the capacitor is directly proportional to the square of the voltage, as shown in the equation U=1/2*C*V^2.

It is possible to create an electrostatic actuator with a repelling force by using the principles of electrostatic potential and voltage differences. This is commonly seen in devices such as electrostatic motors and actuators. I hope this explanation helps clarify your confusion. Let me know if you have any further questions.
 

1. What is electrostatic force?

Electrostatic force is the force that exists between stationary electric charges. This force is responsible for the attraction or repulsion between charged particles.

2. How is electrostatic force calculated?

Electrostatic force is calculated using Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. What is the difference between voltage and electrostatic potential?

Voltage and electrostatic potential are closely related concepts. Voltage is the measure of the difference in electric potential energy per unit charge between two points in an electric field. Electrostatic potential, on the other hand, is the electric potential energy per unit charge at a specific point in an electric field.

4. How is voltage related to electrostatic force?

Voltage is directly related to electrostatic force. The greater the voltage between two points, the greater the electrostatic force between charged particles at those points. This can be seen in the equation V = Ed, where V is voltage, E is the electric field, and d is the distance between the two points.

5. How can electrostatic force be applied in real-life situations?

Electrostatic force has various applications in our daily lives, such as in the functioning of electronic devices like TVs and computers, in the operation of generators and motors, and in the separation of particles in air filters and electrostatic precipitators. It also plays a crucial role in the charging and discharging of batteries and capacitors.

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