Activity: Visualization of Potentials

In introductory physics, you may have learned how to find electrostatic potentials due to several discrete sources by first finding the electric field. However, it is also possible, and often useful, to find electrostatic potentials directly. Using only what you know about the relationship of charges to electrostatic potentials, namely: $$V=\frac{1}{4\pi\epsilon_0} \, \frac{Q}{r}$$ and the superposition principle, sketch the equipotential surfaces for each of the following static charge configurations:

  • Four positive charges arranged in a square.
  • Two positive charges and two negative charges arranged in a square, with like charges diagonally opposite each other.
  • A line segment with constant charge density.
  • A circular loop with constant charge density.

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