# Confusion regarding solution of a problem of conducting spheres

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.

The solution goes like this:

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.

• 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 Commented Jun 19, 2021 at 11:03

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.)