Sphere analogy of non-contact force formulas like electrostatic force should again produce infinite Force when 1 charge of 2 spheres gets closer

Question

Everybody is giving the sphere explaination but 2 touching parts of a sphere, I mean the touching charges in the smallest parts of these spheres that has the smallest charge on it again create infinite EM force between them. You can think it partially. The touching dots on a sphere creates infinite force.

So imagine that two smallest possible charge on these two speres touching each other again, partially the force acting on one another is given by

Again, if these two sphere parts or smallest charge parts come closer to each other the r distance between them continues to become smaller and this goes to infinity by the time they meet each other, or the force becomes crazy big(if they somehow don't touch but come really closer).

In real life, we know that q can not be zero and can not go to zero and it is quantative, it has a definite certain value, but the distance between 2 charges can go to zero as they touch each other.

So, how do we solve or approach this fundamental problem?

Answer 1

The force between two solid spheres of charge is $$F=k\frac{q_1 q_2}{r^2}$$ where $r$ is the distance between the centers of the spheres. This formula applies even if the two spheres are touching (although it does not apply if they overlap).

Although you are right that for the infinitesimal pieces of charge on the surfaces of the spheres at the point of contact the distance is zero, the amount of charge is infinitesimal. So the total force remains finite.