Static Fields 2024 (7 years)
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).
This activity can be paired with activity 29 to find the limiting cases of the potential on the axes of symmetry.
What students learn
 The superposition principle for the electrostatic potential;
 How to calculate the distance formula \(\frac{1}{\vec{r}  \vec{r}'}\) for a simple specific geometric situation;
Electrostatic Potential from Two Charges
 Find a formula for the electrostatic potential \(V(\vec{r})\) that is valid everywhere
in space for the following two physical situations:
 Two charges \(+Q\) and \(+Q\) placed on a line at \(z'=D\) and \(z''=D\).
 Two charges \(+Q\) and \(Q\) placed on a line at \(z'=D\) and \(z''=D\), respectively.
 Simplify your formulas in the limiting cases of:
 the \(x\)axis
 the \(z\)axis
 Discuss the relationship between the symmetries of the physical situations and the symmetries of the functions in these limiting cases.
 Keywords
 Electric potential Point Charges Distance Formula
 Learning Outcomes
