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Learning Introductory Physics with Activities

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

Section 25.4 Representations of Potential

Subsubsection Activities

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Activity 25.4.1. Warm-up.

Consider the equipotentials below.
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An equipotential graph measuring 10 m from top to bottom. A horizontal line at -25 V near the bottom separates lines below that curve down as they move to the right and lines above that curve upward as they move to the right. The topmost line in the upper left corner is at +15 V. Point A lies on the line just below the +15 V line near the left edge, while point B lies two lines above the -25 V line near the right edge.
Figure 25.4.1. Equipotential lines.
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(a)

Draw a vector at each point to indicate the electric field.
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(b)

How can you tell the direction?
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(c)

Which point represents a larger \(\vec{E}\text{?}\)
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(d)

Estimate the magnitude of \(\vec{E}\) at each point.
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Activity 25.4.2. Potential for the Infinite Plate.

The electric field due to the infinite plate with charge density \(\sigma\) shown in the figure below has uniform magnitude and points perpendicular to the plate:
\begin{equation*} \vec{E} = \frac{\sigma}{2\epsilon_0}\hat{z} \end{equation*}
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A plate represented by a vertical line on the left, with point A and D a distance z1 to the right (with D above A) and points B and C a distance z2 to the right, with C above B.
Figure 25.4.2. An infinitely large charged plate.
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(a)

Draw an electric field vector map.
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(b)

Use an integral to find \(\Delta V\) between points A and B.
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(c)

Use an integral to find \(\Delta V\) between points B and C.
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(d)

Draw equipotential lines (at least five!).
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(e)

What happens to the potential if you travel the path:
\begin{equation*} A \rightarrow B \rightarrow C \rightarrow D \rightarrow A \end{equation*}
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Activity 25.4.3. Equipotentials.

Now consider the equipotentials below
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An equipotential graph with x from -3 m to +3 m on the horizontal and y from -3 m to +3 m on the vertical. A 0 V line runs vertically down the center, separating rounded, near-oval potentials on either side, positive up to 20 V on the left, negative down to -20 V on the right.
Figure 25.4.3. Equipotential lines.
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(a)

Rank the points by the value of the potential.
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(b)

Draw a vector at each point to indicate the electric field.
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(c)

Rank the points by the magnitude of the electric field.
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