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Two conducting spheres of radii $r_1$ and $r_2$ are connected by a metallic spring of stiffness $k$ and natural length $ l \gg r_1, r_2$. A positive charge $+Q$ is slowly delivered to any sphere. Find the charge on each sphere. enter image description here

The solution goes like this: enter image description here

But for writing potential of each sphere, why is the potential due the other not taken into account? I can't find a good reason. Please help.

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  • $\begingroup$ I may be wrong but i think since the spheres and the spring are all metallic, the surface of the whole system (including the spheres and the spring ) forms an equipotential surface which is why $V_1=V_2$. It is one of the properties of metals if I am not wrong $\endgroup$ Commented Jun 19, 2021 at 11:03

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Since $l \gg r_1, r_2 $, the other sphere's potential contribution is significantly smaller than the contribution from the main sphere and thus could be approximated to zero. (Coulomb potential is inversely proportional to the distance.)

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  • $\begingroup$ to ignore it there seperation must be large but why we are comparing it with r1 and r2 we should just say it is very large $\endgroup$ Commented Jun 18, 2021 at 9:21
  • $\begingroup$ If you write down the ratio between the potential contributions from each sphere, you'll see that it's not the absolute magnitude, but the relative magnitude of length scales is that matters. $\endgroup$
    – HelloWorld
    Commented Jun 18, 2021 at 9:25
  • $\begingroup$ You mean potential due to sphere itself >>>>> than potential due to other? $\endgroup$ Commented Jun 18, 2021 at 9:40
  • $\begingroup$ Yes, it's right. $\endgroup$
    – HelloWorld
    Commented Jun 18, 2021 at 9:42
  • $\begingroup$ Please add this point to your answer so i can approve it $\endgroup$ Commented Jun 18, 2021 at 10:15

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