Wikipedia says that the magnetic vector potential was discovered by Neumann in 1845, by Weber in 1846 and Lord Kelvin in 1847. It does not mention who discovered the electric scalar potential.
Hence my question - who discovered the electric scalar potential?
(This question has been asked before on this site but only received an answer about the discovery of the gravitational potential.)
Poisson first introduced the scalar potential to electrostatics. He takes it as well-known that, given a force between particles obeying an inverse square law, you can obtain the components of the force by taking partial derivatives of a scalar function equal to the sum of charges divided by their respective distances to that point. He arrives at this from Laplace's work in gravitational potential, and the idea of scalar potential dates back earlier, to Daniel Bernoulli in 1738, as described in this answer about the gravitational potential. In Poisson's first Memoire [note: my own translation of the Memoire], he actually begins the analysis by saying:
(1) Let us consider first a given spheroid, coated in a fluid layer infinitely thin and of variable thickness; let us suppose that the molecules of this fluid repel each-other mutually in inverse proportion to the square of their separation, and let us attempt to determine the total action of the layer on one of these molecules, or more generally on a given point of space, taken outside or inside of the spheroid. We know that the components of the attraction or the repulsion which a body exerts on a given point, are expressed by the partial differences* of a certain function of the coordinates of this point, which is to say, of the function which represents the sum of the molecules of the body, divided by their respective distances to the given point: let us designate this sum by V , relative to the fluid layer which we are considering, and let us determine the value of V as a function of the coordinates of a given point in space.
* differences partielles, meaning partial derivatives
In modern notation, let $q$ be the charge of a "molecule" of electricity, and $\mathbf{r}_i$ be the position vector of a given molecule, and suppose we want to find the force at a point $\mathbf{r}$ due to all molecules. What Poisson is saying is, given a function $V$ defined as: $$ V(\mathbf{r})=\sum_i \frac{q}{|\mathbf{r_i}-\mathbf{r}|}, $$ we can obtain the force vector $\mathbf{F}$ per unit charge at $\mathbf{r}$ by taking the gradient of $V$, i.e. we obtain the electric field $\mathbf{E}(\mathbf{r})$, $$ \mathbf{E}(\mathbf{r}) = \nabla V. $$
Poisson goes on to derive the electric potential between two spheres of different radii separated by large and small distances. His derivation of the potential between two spheroids is clearly the main subject of his Memoires, and his use of the potential is just a mathematical tool he introduces in his assumptions, so while he was the first to apply the concept of scalar potential to electrostatics, it's also worth noting that he had little to do with the origin of the concept of potential itself. George Green's work in An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (1828) (described on Wikipedia, and available on Google Books) was far more important in the development of the theory of potentials, for introducing a number of significant results, which now bear his name.
