---
title: "Two equipotential surfaces in a region of non-uniform electric field have potentials \\(V_A = 60\\text{ V}\\) and \\(V_B = 20\\text{ V}\\), as shown in the diagram. A point charge \\(+q\\) is moved from the \\(V_A\\) surface to the \\(V_B\\) surface along four distinct paths labeled 1, 2, 3, and 4. Path 1 is a direct straight path in a region of higher electric field magnitude, Path 2 is a direct straight path in a region of lower electric field magnitude, Path 3 is a smooth curved path, and Path 4 is an indirect winding path. Which of the following correctly ranks the work \\(W_1\\), \\(W_2\\), \\(W_3\\), and \\(W_4\\) done by the electric field on the charge along each path?"
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url: "https://nerd-notes.com/ubq/121076/"
date_modified: "2026-08-23T04:57:42+00:00"
---

# Two equipotential surfaces in a region of non-uniform electric field have potentials \(V_A = 60\text{ V}\) and \(V_B = 20\text{ V}\), as shown in the diagram. A point charge \(+q\) is moved from the \(V_A\) surface to the \(V_B\) surface along four distinct paths labeled 1, 2, 3, and 4. Path 1 is a direct straight path in a region of higher electric field magnitude, Path 2 is a direct straight path in a region of lower electric field magnitude, Path 3 is a smooth curved path, and Path 4 is an indirect winding path. Which of the following correctly ranks the work \(W_1\), \(W_2\), \(W_3\), and \(W_4\) done by the electric field on the charge along each path?

Two equipotential surfaces in a region of non-uniform electric field have potentials \(V_A = 60\text{ V}\) and \(V_B = 20\text{ V}\), as shown in the diagram. A point charge \(+q\) is moved from the \(V_A\) surface to the \(V_B\) surface along four distinct paths labeled 1, 2, 3, and 4. Path 1 is a direct straight path in a region of higher electric field magnitude, Path 2 is a direct straight path in a region of lower electric field magnitude, Path 3 is a smooth curved path, and Path 4 is an indirect winding path. Which of the following correctly ranks the work \(W_1\), \(W_2\), \(W_3\), and \(W_4\) done by the electric field on the charge along each path?

![A two-dimensional diagram showing two curved dashed lines representing equipotential surfaces. The left dashed curve is labeled \(V_A = 60\text{ V}\) at its top end. The right dashed curve is labeled \(V_B = 20\text{ V}\) at its top end. The two dashed curves are closer together at the top and gradually separate farther apart toward the bottom. Four solid lines with arrowheads represent paths starting on the left dashed curve and ending on the right dashed curve. Path 1 is a short horizontal straight segment near the top, labeled 1. Path 2 is a longer horizontal straight segment near the bottom, labeled 2. Path 3 is an upward-curved line in the middle region, labeled 3. Path 4 is a serpentine S-shaped line located between paths 2 and 3, labeled 4. Each path starts at a solid circular point on curve \(V_A\) and ends with an arrowhead on curve \(V_B\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461061-z0bNaB.jpg)

- **A.** \(W_1 = W_2 = W_3 = W_4\)
- **B.** \(W_1 > W_2 > W_3 > W_4\)
- **C.** \(W_4 > W_3 > W_2 > W_1\)
- **D.** \(W_1 = W_2 > W_3 = W_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121076/*