The Laplace operator has many applications in the physical sciences, one of which being in electric potentials. An electric field, $E$, is defined as a vector field that describes the force of electricity per unit charge on any charge in the field. Take, for example, an electric field created by a point charge at $(0,0)$. By Coulumb's law:

$E = \frac{F}{q} \\ F = \large\frac{Qq}{4\pi\epsilon_{0}r^{2}} \\ E = \large\frac{Qq}{4\pi\epsilon_{0}r^{2}} \cdot \frac{1}{q} \\ E = \large\frac{Q}{4\pi\epsilon_{0}r^{2}}$

where $Q$ is the charge of the point charge, $q$ is the charge of a charge in the field, $r$ is the distance of the charge from the point charge, and $\epsilon_0$ is vacuum permittivity, a physical constant approximately equal to $8.8$ x $10^{-12}$ Farads per meter.

## Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood