# Basic confusion about fields and infinite potential

Consider a system of two electrically charged particles. Their charge doesn’t matter for my question but suppose they are both positive.

I am confused about what the correct way to calculate forces on particles is, based on information of the field, when those particles themselves contribute to the field and are at an infinite potential: What is wrong with the following argument?

Particle 1 will contribute to the electric field potential proportional to $$\frac 1 {d}$$, where $$d$$ is the distance from particle 1. But at particle 1’s position, the distance is $$0$$, so that the electric potential is infinite at that point. Hence, the gradient of the electric potential is undefined there, and we cannot compute a force on particle 1, even though we would want a force from particle 2 to be exerted.

• That's write. You might want to add the formula $F_{12} = q_1 \cdot E_2 \propto \frac{q_1 \cdot q_2}{r_{12}^2}$. Commented Jun 15, 2020 at 17:32