Student handout: Electrostatic Potential Due to a Pair of Charges (without Series)

AIMS Maxwell 2021
  • 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;
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:
    • Two charges \(+Q\) and \(+Q\) placed on the z-axis at \(z'=D\) and \(z'=-D\).
    • Two charges \(+Q\) and \(-Q\) placed on the z-axis at \(z'=D\) and \(z'=-D\), respectively.
  • Simplify your formulas for the special 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 special cases.

Keywords
Electric potential Point Charges Distance Formula
Learning Outcomes