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When two conductors (let's say spherical) of charges $q_1$ and $q_2$ and radii $r_1,r_2$ respectively are brought and connected by a metal rod,we know that flow of charge occurs unless potentials are the same. And the conventional method of doing this is by equating the potentials of the two separate spheres where the formula $\frac{Kq_1}{r_1}=\frac{kq_2}{r_2}$ is used. But this formula is true considering when there is only charge $Q$. When another charge is brought close,wont the potential due to the other charge be considered as well? So,what I am asking is why is the potential of the sphere $q_1$ still $\frac{kq_1}{r_1}$ instead of $\frac{kq_1}{r_1}+\frac{kq_2}{d}$ where $d$ is the distance from the center of the $2nd$ sphere to the surface of the $1st$ sphere. The same applies for the potential of the $2nd$ sphere.

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  1. For a sphere charged with a total charge ( Q ), the potential at a point located at a distance ( r > R ) (where ( R ) is the sphere's radius) from the sphere's center is given by ( \frac{kQ}{r} ). This formula is valid only when the charge ( Q ) is uniformly distributed across the sphere's surface.

  2. In a conductor, the distribution of charge is such that the potential remains constant at every point on the conductor, provided the conductor is in electrostatic equilibrium.

  3. When multiple charge distributions are present, the potential at any given point is the sum of the potentials contributed by each individual charge distribution.

  4. Consider a charged spherical conductor. If a point charge is introduced near this conductor, the charge distribution on the sphere will become non-uniform. This is because the point charge will not produce a uniform potential across the sphere's surface. Specifically, the point charge will attract opposite charges closer to itself and repel like charges further away.

Now, addressing the scenario with two spherical charged conductors:

When two charged spherical conductors are placed in proximity to each other, the charge distribution on each sphere becomes non-uniform. This non-uniformity arises because one sphere's potential does not contribute uniformly to the other sphere's surface. Calculating the potential considering this non-uniform distribution can be mathematically intricate. Therefore, in textbook problems, it's often assumed that the conductors are sufficiently distant from each other, allowing for the simplification that their charge distributions remain uniform. Under this assumption, the potential of one sphere can be calculated using the formula from the first point without needing to consider the combined effect of both spheres. This is because, at an infinite distance, the potential contribution from one sphere to the other is negligible.

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