Skip to main content

Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 24.7 Challenge - Equipotential Surfaces

A*R*C*S 24.7.1. Infinite Wires.

Two infinite wires are located parallel to the y-axis. One wire has uniform charge density \(+\lambda\) and is located at \(x = +x_o\text{.}\) The other wire has uniform charge density \(-\lambda\) and is located at \(x = -x_o\text{.}\) The electric potential in the \(xy\)-plane for this system is given by:
\begin{equation*} V(x, y) = 2k \lambda \ln{|x + x_o |} - 2k \lambda \ln{|x-x_o |} = 2k \lambda \ln{| \frac{x + x_o }{x - x_o} |} \end{equation*}
Complete the following tasks as part of your ARCS solution:
  1. Physical representation: Create an accurate equipotential graph in the \(xy\)-plane and the corresponding electric field vector map.
  2. Calculate: Find the electric field at every point in the \(xy\)-plane.
  3. Sensemaking: Show that your electric field is what you expect from the superposition of two infinite line charges.

Explanation 24.7.2. Equipotential Graph II.

Figure 24.7.1. Equipotential graph in the xy-plane.
This problem is a modified Explanation Task with several specific prompts. Above is a graph of the equipotentials due to some unknown distribution of charges. The boxed numbers represent the values of the potential.
  1. Sketch vectors at the indicated points that represent the electric field \(\vec{E}\text{.}\) Both the direction and the magnitude of your vectors should be qualitatively correct. Describe how you determined your answers.
  2. Explicitly rank the magnitudes of the electric field vectors you drew. Describe how you determined your answers.
  3. Sketch a charge diagram, using + and - to indicate the locations where you expect there to be positive and negative charges, respectively. Justify your answers.
  4. Imagine that you are a charged particle moving along the vertical line that passes through points C, D, and E (the \(y\)-axis).
    1. Sketch a graph of the electric potential \(V\) as a function of \(y\text{.}\)
    2. On a different set of axes, sketch the \(y\)-component of the electric field \(E_y\) as a function of \(y\text{.}\)
    3. Discuss the relationship between your two graphs.

A*R*C*S 24.7.3. Capacitance and Charge.

Two parallel 3.0-cm-diameter flat aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 50 V battery. Find the capacitance and the magnitude of the charge on each electrode.

Subsection Metacognitive Reflection

PrevTopNext