Students work in small groups to use the superposition principle \[V(\vec{r}) =\frac{1}{4\pi\epsilon_0}\int\frac{\rho(\vec{r}^{\,\prime})}{\vert \vec{r}-\vec{r}^{\,\prime}\vert} \, d\tau^{\prime}\] to find an integral expression for the electrostatic potential, \(V(\vec{r})\), everywhere in space, due to a ring of charge.
In an optional extension, students find a series expansion for \(V(\vec{r})\) either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension.
Use the superposition principle for the electrostatic potential due to a continuous charge distribution: \begin{align} V(\vec{r})=\frac{1}{4\pi \epsilon_0} \int \frac{\rho'(\vec{r}^{\,\prime})}{\left| \vec{r}-\vec{r}'\right|}\, d\tau', \end{align} to find the electrostatic potential everywhere in space due to a uniformly charged ring with radius \(R\) and total charge \(Q\).
Check with a teaching team member before moving on to subsequent parts below.