Timeline for Charge conservation and the physical significance of image charges
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2023 at 3:51 | comment | added | knzhou | Certainly, you can think of it that way! | |
| Nov 23, 2023 at 2:54 | comment | added | Jonathan Huang | So the problem isn't that the charge is not conserved, but that what we fixed at the start wasn't the charge, but the potential $V_1$, and the series of approximations tells us the charge $Q^{(1)}$ that is needed to produce such a potential? | |
| Nov 23, 2023 at 2:51 | comment | added | knzhou | For example, suppose I was trying to find increasingly good approximations to the energy of a particle. The leading term is $E_0 = mc^2$. The first correction is $E_1 = mv^2/2$. The total answer is $E = E_0 + E_1 + \ldots = mc^2/\sqrt{1-v^2/c^2}$. Your question is analogous to saying: "Wait a second! $E$ is bigger than $E_0$! Doesn't your argument violate conservation of energy?" | |
| Nov 23, 2023 at 2:47 | comment | added | knzhou | Smythe is just trying to find a self-consistent solution to the equations. The sum of all the $Q_n$ is the physical charge on the sphere. The quantity $Q_1$ has no physical meaning. It is just some auxiliary quantity that you define early on in the argument, but only the result of the full argument has meaning. | |
| Nov 23, 2023 at 2:11 | comment | added | Jonathan Huang | @Triatticus $Q^{(1)}_n$ is always positive, so the sum of the series must be larger than $Q^{(1)}_1$. | |
| Nov 23, 2023 at 2:10 | history | edited | Jonathan Huang | CC BY-SA 4.0 |
grammar nuissance
|
| Nov 23, 2023 at 2:10 | comment | added | Jonathan Huang | @LPZ yes, that is what I mean. I edited the sentence. | |
| Nov 22, 2023 at 23:47 | comment | added | LPZ | What do you mean by the charge you started with ? Did you mean write in the last equation: $$Q^{(1)}=Q_1^{(1)}$$ if not, what is $Q$? | |
| Nov 22, 2023 at 22:23 | comment | added | Triatticus | How did you come to the conclusion that the charge is more? Did you explicitly evaluate that series? | |
| Nov 22, 2023 at 18:20 | history | asked | Jonathan Huang | CC BY-SA 4.0 |