This question is about the generalization of Coulomb's law to continuous bodies of charge. The basic statement of Coulomb's Law involves two discrete charges $q_1$ an $q_2$:
$$\vec{F}_i = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{12}} \hat{r}_i $$
Here $i$ represents the charge on which the force is exerted, and $\hat{r}_i$ represents the unit displacement vector between the other charge and the charge $i$.
Many treatment of electrostatics extend this law to the case that one charge is not discrete, but rather a continuous body. The force on the discrete charge $Q$ is then:
$$\vec{F} = \frac{Q}{4 \pi \epsilon_0} \int \frac{dq}{r^2} \hat{r} $$
Here $dq$ is the infinitesimal charge element of the continuous body, while $r$ and $\hat{r}$ represent the distance and displacement vectors between $dq$ and $Q$.
Continuing this way, we could probably propose an expression for force between two continuous bodies of charge, like so:
$$\vec{F} = \frac{1}{4 \pi \epsilon_0} \int \int \frac{dq_1 dq_2}{r^2} \hat{r}$$
However, I have not really seen this expression in the literature/treatments of electrostatics. Does anyone know why this is the case? Is the expression not useful, or are there no applications demanding the above expression?