Is this an application of the Virial theom?

In summary, the conversation discusses a problem involving an infinitely long liquid column with radius R connected to an electric potential V and a surface charge density. A small perturbation in the surface profile of the column can cause a change in the surface charge density, resulting in a change in the electric energy of the column by E. The overall change in electric potential is -E, which raises the question of whether the Virial theorem can explain this result or if another theorem or calculation is needed. It is clarified that the Virial theorem is typically used in dynamics, not statics problems. The conversation ends with the speaker mentioning their need for an explanation for the energy change in their specific problem.
  • #1
weiwei
The problem concerns a liquid column (assume infinitely long) with radius R connected to an electric potential V, the liquid thus has certain surface charge density.
A small perturbation may change the surface profile of the cylinder (small compared to R) and thus change its surface charge density.
This change causes electric energy of the liquid column to change by E, then the energy change of the charging system is -2E, making the total electrical potential change E-2E = -E. Can Virial theorem explain this result? If not what theorem (or calculation) explains it?
 
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  • #2
Isn't the virial theorem used in dynamics, not statics problems? Maybe you're confusing it with calculus of variations?
 
  • #3
hilbert2 said:
Isn't the virial theorem used in dynamics, not statics problems? Maybe you're confusing it with calculus of variations?
Thanks for your reply. I am dealing with a problem of instability of an infinitely long charged liquid jet. When there is a change is surface profile(which originally is a column with radius R), the electric energy change of the liquid jet is E, the charging system (a constant voltage V connected to the liquid jet) has energy change -2E, the paper I am reading just gives this result without proving it. So I am trying my luck here to see if any theorem can explain it.
 

1. What is the Virial theorem?

The Virial theorem is a mathematical relationship that describes the behavior of a system of particles in equilibrium. It states that the average kinetic energy of a system is equal to half of the average potential energy.

2. How is the Virial theorem applied in science?

The Virial theorem has various applications in different fields of science, such as astrophysics, statistical mechanics, and quantum mechanics. It is used to study the behavior of galaxies, stars, and other celestial bodies, as well as the properties of gases and other systems at the microscopic level.

3. Can the Virial theorem be used to predict the behavior of a system?

Yes, the Virial theorem can be used to make predictions about the behavior of a system. By applying the theorem, scientists can determine the relationship between the kinetic and potential energies of a system and use it to understand its overall behavior.

4. Is the Virial theorem a fundamental law of nature?

No, the Virial theorem is not a fundamental law of nature. It is a mathematical relationship that has been derived from other fundamental physical laws, such as Newton's laws of motion and the law of conservation of energy.

5. Are there any limitations to the application of the Virial theorem?

Yes, there are some limitations to the application of the Virial theorem. It is mainly applicable to systems in equilibrium and does not take into account factors such as external forces and non-conservative interactions. It also assumes that the system is isolated, meaning that there is no exchange of energy with the surroundings.

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