Calculation of the Coulomb electrostatic potential created by a uniformly charged square on its plane: Exact mathematical formulas

We calculate exactly the Coulomb electrostatic potential created by a uniformly charged square on its plane. The chosen solution method leads to certain types of integral expressions which involve combinations of products of error functions and power functions. These type of integrals that should be solved are not standard ones, therefore, the integration formulas we derive in the process may be deemed of mathematical interest on their own right. Use of these formulas enables us to derive an exact analytic expression for the Coulomb electrostatic potential created by a uniformly charged square at an arbitrary point on its plane.

► Exact Coulomb electrostatic potential created by a uniformly charged square. ► Coulomb electrostatics potential on the two-dimensional plane of the square. ► Non-standard integral expressions with combinations of error and power functions. ► Results can be of interests to studies of electrostatic or mathematical physics.