group Small Group Activity
60 min.
Static Fields 2022 (4 years)
electrostatic potential multipole charge symmetry scalar field superposition coulomb's Law
Power Series Sequence (E&M)
Ring Cycle Sequence
Students work in small groups to use the superposition principle
\[V(\vec{r}) = \frac{1}{4\pi\epsilon_0}\sum_i \frac{q_i}{\vert\vec{r}-\vec{r}_i\vert}\]
to find the electrostatic potential \(V\) everywhere in space due to a pair of charges (either identical charges or a dipole).
Different groups are assigned different arrangements of charges and different regions of space to consider: either on the axis of the charges or in the plane equidistant from the two charges, for either small or large values of the relevant geometric variable.
Each group is asked to find a power series expansion for the electrostatic potential, valid in their group's assigned region of space.
The whole class wrap-up discussion then compares and contrasts the results and discuss the symmetries of the two cases.