The electric field $\bf{E}$ represents how much force would act on a particle at a certain position per unit charge. However, if we actually place a particle in that position, the electric field will have a singularity there (because of the $\frac{1}{r^2}$ in Coulomb's law). Isn't this kind of a paradox? In my eyes, this makes the concept of electric field useless, because it cannot be used to calculate the force on a particle.

The electric field $\bf{E}$ represents how much force would act on a particle at a certain position per unit charge. However, if we actually place a particle in that position, the electric field will have a singularity there (because of the $\frac{1}{r^2}$ in Coulomb's law). Isn't this kind of a paradox? In my eyes, this makes the concept of electric field useless, because it cannot be used to calculate the force on a particle.

The electric field $\bf{E}$ represents how much force would act on a particle at a certain position per unit charge. However, if we actually place a particle in that position, the electirc field will have a singularity there (because of the $\frac{1}{r^2}$ in Coulomb's law). Isn't this kind of a paradox? In my eyes, this makes the concept of electric field useless, because it cannot be used to calculate the force on a particle.

The electric field $\bf{E}$ represents how much force would act on a particle at a certain position per unit charge. However, if we actually place a particle in that position, the electric field will have a singularity there (because of the $\frac{1}{r^2}$ in Coulomb's law). Isn't this kind of a paradox? In my eyes, this makes the concept of electric field useless, because it cannot be used to calculate the force on a particle.