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?
group Small Group Activity
30 min.
group Small Group Activity
30 min.
group Small Group Activity
60 min.
Mechanics Gravitational Potential Energy Zero of Potential Introductory Physics
Students examine a plastic “surface” graph of the gravitational potential energy of an Earth-satellite system to explore the properties of gravitational potential energy for a spherically symmetric system.keyboard Computational Activity
120 min.
electrostatic potential python
Students write python programs to compute and visualize the potential due to four point charges. For students with minimal programming ability and no python experience, this activity can be a good introduction to writing code in python usingnumpy
and matplotlib
.
group Small Group Activity
30 min.
computer Mathematica Activity
30 min.
group Small Group Activity
30 min.
assignment Homework
Find the electrostatic potential at a point \(\vec{r}\) on the \(x\)-axis at a distance \(x\) from the center of the quadrupole.
A series of charges arranged in this way is called a linear quadrupole. Why?
group Small Group Activity
30 min.
group Small Group Activity
30 min.
Mechanics Gravitational Force Gravitational Potential Energy Derivatives Introductory Physics
Students examine a plastic "surface" graph of the gravitational potential energy of a Earth-satellite system to make connections between gravitational force and gravitational potential energy.