Recent content by jkfjbw

How did you get ##\rho=E\epsilon_0##? Is this supposed to be the differential form of Gauss' law? You'd get infinity for the ##\nabla\cdot\vec{E}## due to the surface charge.

I agree, however it was asked of me to "Forget the word capacitance for a moment", therefore divorcing the rest of bob012345's stated scenario from the context of capacitance and the expectations that accompany it.

Poisson's equation gives uniqueness of the potential provided the charge density function is given, however the situation in question is comparing the two different charge density functions resulting from depositing two different charges on the same conductors. Poisson's equation does not...

I think this assessment is incorrect. The field of the brought-in charge permeates through all of space, so if the brought-in charge is in the vicinity of the conductor, the electric field near the conductor will be appreciably changed. If you bring in a unit test charge from infinity in order...

Are you saying that for any point ##P_1## on the surface of the conductor and ##P_2## an arbitrary point outside the conductor, ##V_\text{old}(P)## the initial voltage as a function in terms of a point in space and ##V_\text{new}(P)## the latter voltage as a function in terms of a point in...

Yes, I was.

I agree that the potential anywhere on or in the conductor is the same, given that this is an electrostatic situation. I do not think the potential of the conductor directly correlates to the total charge on the conductor. If you have a conductor with charge ##Q_1## it will have a potential...

I mean the ##\rho(x,y,z)## function in Poisson's equation that gives the charge density as a function of position. I'm not sure how to describe this function for a parallel plate capacitor as the plates have surface charges and surface charges present difficulties when taking derivatives, but I...

This is nothing but hand-waving. Please read the prior posts. Yes, it is a definition but it is more than just a definition. There is also a claim being made.

It seems that the arguments being presented rely on the charge distribution function increasing by the same constant factor that the total charge on one of the conductors is increased, but how do we know that the charge will distribute itself in that way? If this were an insulator you could...

Yes, I agree that if you do not consider the capacitance to be a constant then there is nothing to prove, however all of my physics E&M textbooks claim that it is a constant, and this is what I am trying to prove. I'm not following your argument. Yes, I do see how you can calculate the...

I do understand his point, but he is also wrong in making it. All of my eletromagnetism books define the capacitance as a constant value. That is what I am asking a proof for. Clearly, if you do not consider the capacitance to always be a constant value then there is nothing to prove, however...

I do not have a counterexample in mind, but the onus of proof is not on me to disprove the claim, rather the onus of proof is on those who claim it is true in the first place.

Q=CV is more than just a definition. It is also an assertion that the ratio of the charge to the potential difference is a constant.

What is a proof of the formula Q=CV for a capacitor with arbitrary but unchanging shape where C is a constant?