Does the virial theorem explain charged liquid column perturbations?

[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?

 

[hilbert2]

Isn't the virial theorem used in dynamics, not statics problems? Maybe you're confusing it with calculus of variations?

 

[weiwei]

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.