Students are prompted to consider the scalar superposition of the electric potential due to multiple point charges. First a single point charge is discussed, then four positive charges, then an electric quadrupole. Students draw the equipotential curves in the plane of the charges, while also considering the 3D nature of equipotentials.
Start with a Simpler Case: The electrostatic potential due to a particle with charge \(q\) is: \[V(r)=\frac{kq}{r}\]
where \(k\) is the electrostatic constant and \(r\) is the distance from the particle.
On your whiteboard, identify all the points with the same value of potential around a single point charge. Repeat for several different values of potential.
Add Complexity: Draw equipotential surfaces for the potential due to 4 particles with equal, positive charge arranged in a square.
Examine a New Case: Repeat for a quadrupole: 2 positively charged particles and 2 negatively charged particles arranged in a square, with “like” charged particles on opposite corners.
Extend to New Surfaces: The red surface represents the potential of a quadrupole in the plane of the charges (at \(z=0\) cm). What would the potential look like in the \(z=1\) cm plane? What would be different? What about the \(z=-1\) cm?