- Students need to understand that the surface represents the electric potential in the center of a parallel plate capacitor. Try doing the activity Electric Potential of Two Charged Plates before this activity.
- Students should know that
- objects with like charge repel and opposite charge attract,
- object tend to move toward lower energy configurations
- The potential energy of a charged particle is related to its charge: \(U=qV\)
- The force on a charged particle is related to its charge: \(\vec{F}=q\vec{E}\)
Before you is a plastic surface and a contour map each representing the electric potential. A \(1\)-\(cm\) height difference corresponds to an electric potential difference of \(1~V\).
Consider the Motion of a Positive Charge: If you were to place a positively charged particle at rest at the blue square, which way do you expect the particle to move?
Does the electric potential energy increase, decrease, or stay the same?
Consider the Motion of a Negative Charge: If you were to place a negatively charged particle at rest at the blue square, which way do you expect the negative charged particle to move?
Consider the Electric Field at the Blue Square: Draw a vector on the contour map to indicate \(\vec{E}\) at the blue square.
Does your answer depend on the sign of the charge?
How is the vector oriented with respect to the contour lines?
Consider the Electric Field at Several Points: Draw vectors at several additional points to represent \(\vec{E}\), making sure the lengths of the vectors are qualitatively accurate. Choose points near the middle and edges of the map.
How do the electric field vectors near the middle compare with the vectors near the edge of the map?
How are the electric field vectors related to the equipotential lines?
group Small Group Activity
30 min.
assignment Homework
group Small Group Activity
30 min.
keyboard Computational Activity
120 min.
assignment Homework
group Small Group Activity
30 min.
group Small Group Activity
30 min.
coulomb's law electric field charge ring symmetry integral power series superposition
Students work in groups of three to use Coulomb's Law \[\vec{E}(\vec{r}) =\frac{1}{4\pi\epsilon_0}\int\frac{\rho(\vec{r}^{\,\prime})\left(\vec{r}-\vec{r}^{\,\prime}\right)}{\vert \vec{r}-\vec{r}^{\,\prime}\vert^3} \, d\tau^{\prime}\] to find an integral expression for the electric field, \(\vec{E}(\vec{r})\), everywhere in space, due to a ring of charge.
In an optional extension, students find a series expansion for \(\vec{E}(\vec{r})\) either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension.
group Small Group Activity
120 min.
assignment Homework
Consider a collection of three charges arranged in a line along the \(z\)-axis: charges \(+Q\) at \(z=\pm D\) and charge \(-2Q\) at \(z=0\).
assignment Homework
Consider the finite line with a uniform charge density from class.