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Learning Introductory Physics with Activities

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

Section 24.6 Practice - Equipotential Surfaces

Subsection Explanation Practice

Explanation 24.6.1. Equipotential Graph I.

Figure 24.6.1. Equipotential graph in the xy-plane.
You acquire a wire that has the equipotential graph above. Rank the three indicated points (P, Q, and R) by the magnitude of the electric field from greatest to smallest.

Explanation 24.6.2. Equipotential Graph II.

Describe the charge distribution of the equipotential graph above.

Subsection A*R*C*S Practice

A*R*C*S 24.6.3. Capacitor in an Air Conditioner.

A large capacitor in an air conditioner is typically connected to the potential difference provided to your house (120 V). Although capacitors like this are usually cylindrical, model this one as a parallel plate capacitor with square plates separated by 2.0 mm. If you want your capacitor to store 0.25 J of energy, what is the area of the capacitor plates? How feasible do you think this answer is?

Subsection Numerical Practice

Calculation 24.6.4. Equipotential Graph.

The figure below shows a map of equipotential lines. The potential values for lines a, b, and c are 10 V, 20 V and 30 V respectively. If you release an electron on equipotential line b, which direction will it move?
Figure 24.6.2. Diagram of equipotential lines for an unknown charge distribution.
Answer.
Toward c.

Calculation 24.6.5. Equipotential Lines around Conductors.

The sketch below shows equipotential lines (which are cross-sections of equipotential surfaces) between two charged conductors (shown in solid black). Various points on the equipotential lines near the conductors are labeled A, B, C, …, I. Each question regarding this situation has one correct answer.
Figure 24.6.3. Diagram of equipotential lines around two charged conductors.
  1. Which conductor is positively charged?
  2. At which of the labeled points does the electric field have the greatest magnitude?
  3. At which of the labeled points would an electron have the greatest potential energy?
  4. What is the potential difference between points B and E?
  5. What is the direction of the electric field at B?
  6. A positive point charge is placed, initially at rest, at F. When it is released, what happens to the motion of the point charge?
Answer 1.
R
Answer 2.
I
Answer 3.
H
Answer 4.
50 V
Answer 5.
Toward D.
Answer 6.
A force will cause it to move toward H.

Calculation 24.6.6. Zero Electric Potential.

If the electric potential value at a point in space is zero, does that mean the electric field value at that point must be zero, as well? Explain.
Answer.
No. At each point, the electric field value is proportional to the change in electric potential value (compared to a nearby point).

Calculation 24.6.7. Voltmeter.

The electric field in a certain region of space is a consistent value of \(\vec{E} = (-8 \ \mathrm{N}/\mathrm{C})\hat{x}\text{.}\) Suppose you place the probes of a voltmeter along the x-axis, 2.00 cm apart, in that region. What is the magnitude of the reading on the voltmeter?
Answer.
0.16 V

Calculation 24.6.8. Electrostatic Equilibrium.

Consider a piece of metal (a conductor) that has come to electrostatic equilibrium in a steady, external electric field. Which of the following statements are true?
  1. The electric potential everywhere on a conductor is the same value.
  2. The net electric field inside the conductor is zero.
  3. The net electric field outside the conductor is not zero.
  4. The external electric field polarizes the free electrons in the metal, generating an internal electric field that opposes and cancels out the external field.
Answer.
(1), (2), (3), (4)

Calculation 24.6.9. Strength of the Electric Field.

What is the strength of the electric field in a region where the electric potential is constant?
Answer.
The electric field strength is zero because electric potential differences are directly related to the field strength. If the potential difference is zero, then the field strength must also be zero.

Calculation 24.6.10. Building Hydrogen.

To form a hydrogen atom, a proton is fixed at a point and an electron is brought from far away to a distance of \(0.529 \times 10^{-10} \ \mathrm{m}\text{,}\) the average distance between proton and electron in a hydrogen atom. How much work is done?
Answer.
\(4.35 \times 10^{-18} \ \mathrm{J}\)

Calculation 24.6.11. Equivalence of Units.

Show that units of V/m and N/C for electric field strength are indeed equivalent.
Answer.
\(1 \ \mathrm{V} = 1 \ \frac{J}{C}\text{;}\) \(1 \ \mathrm{J} = 1 \ \mathrm{Nm} \rightarrow 1 \ \frac{\mathrm{V}}{\mathrm{m}} = 1 \ \frac{\mathrm{N}}{\mathrm{C}}\)

References References

[1]
Practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.
[2]
Practice activities provided by Ling, S. J., Moebs, W., & Sanny, J. (2016). Electric Potential. In University Physics Volume 2. OpenStax.
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