Recall that the electrostatic potential $V$ due to a point charge $q$ stationary at the origin is given by \begin{equation} V = \frac{1}{4\pi\epsilon_0} \> \frac{q}{r} \label{vpt} \end{equation} where $r$ is the distance from the point charge to the place at which the potential is being evaluated. Similarly, the gravitational potential $\Phi$ due to a point mass $m$ is given by \begin{equation} \Phi = -G \> \frac{m}{r} \end{equation} In the coming sections of the text, we will be discussing both the physical meaning of these potentials and how to calculate them.

The constant $\epsilon_0$ is called the permittivity of free space. The constant $G$ is called Newton's constant. In SI units, the values of these constants and their dimensions are:

\begin{eqnarray*} \epsilon_0 &=& 8.85\times10^{-12}\frac{\rm C^2}{\rm Nm^2} \\ &\sim& \frac{\rm C^2}{\rm M\frac{L}{T^2}L^2} = \frac{\rm C^2T^2}{\rm ML^3} \\ G &=& 6.67\times10^{-11}\frac{\rm Nm^2}{\rm kg^2} \\ &\sim& \frac{\rm M\frac{L}{T^2}L^2}{\rm M^2} = \frac{\rm L^3 }{\rm MT^2} \\ \end{eqnarray*} (How did we calculate their dimensions?)

From this information, you should be able to show that the potentials themselves have the following dimensions: \begin{eqnarray*} V &\sim& \frac{\rm ML^2}{\rm CT^2} \\ \Phi &\sim& \frac{\rm L^2}{\rm T^2} \end{eqnarray*}