group Small Group Activity
30 min.
AIMS Maxwell AIMS 21
AIMS Maxwell AIMS 21
Static Fields Winter 2021
electrostatic potential charge linear charge density taylor series power series scalar field superposition symmetry distance formula
Power Series Sequence (E&M)
Ring Cycle Sequence
Students work in groups of three 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.