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group Small Group Activity

30 min.

Work By An Electric Field (Contour Map)

E&M Path integrals

Students will estimate the work done by a given electric field. They will connect the work done to the height of a plastic surface graph of the electric potential.

group Small Group Activity

30 min.

Electric Field of Two Charged Plates
  • 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 a Parallel Plate Capacitor” before this activity.
  • Students should know that
    1. objects with like charge repel and opposite charge attract,
    2. object tend to move toward lower energy configurations
    3. The potential energy of a charged particle is related to its charge: \(U=qV\)
    4. The force on a charged particle is related to its charge: \(\vec{F}=q\vec{E}\)

group Small Group Activity

30 min.

Electric Field Due to a Ring of Charge

coulomb's law electric field charge ring symmetry integral power series superposition

Power Series Sequence (E&M)

Ring Cycle Sequence

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.

assignment Homework

Electric Field from a Rod
Consider a thin charged rod of length \(L\) standing along the \(z\)-axis with the bottom end on the \(xy\)-plane. The charge density \(\lambda\) is constant. Find the electric field at the point \((0,0,2L)\).

assignment Homework

Line Sources Using Coulomb's Law
  1. Find the electric field around a finite, uniformly charged, straight rod, at a point a distance \(s\) straight out from the midpoint, starting from Coulomb's Law.
  2. Find the electric field around an infinite, uniformly charged, straight rod, starting from the result for a finite rod.

assignment Homework

Central Force

Which of the following forces can be central forces? which cannot?

  1. The force on a test mass \(m\) in a gravitational field \(\vec{g~}\), i.e. \(m\vec g\)
  2. The force on a test charge \(q\) in an electric field \(\vec E\), i.e. \(q\vec E\)
  3. The force on a test charge \(q\) moving at velocity \(\vec{v~}\) in a magnetic field \(\vec B\), i.e. \(q\vec v \times \vec B\)

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