Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure below. Which statement about the electric potential is true?

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BlackTom AI · Accepted Answer

E = -dV/dx so the electric potential decreases in the direction of the electric field; for a uniform field to the right, V is a linear function V(x) = -Ex + constant (with E > 0 pointing right). This is the key relation linking field direction and how potential changes with horizontal position. Step-by-step reasoning: 1. Use the differential relation: E_x = -dV/dx. For a uniform field pointing right, E_x = +E (a positive constant). Therefore dV/dx = -E, which is negative. That means as x increases (moving to the right) the potential V(x) decreases at a constant rate. 2. Identify the horizontal positions of the points: points A and B lie directly one above the other (same x coordinate), while C is to the right (larger x coordinate). The electric potential in this uniform field depends only on x, not on vertical position y. 3. Because A and B share the same x, V(A) = V(B). Because C has a larger x, V(C) = V(A) + dV where dV = -E (x_C - x_A) < 0, so V(C) < V(A). Illustrative numbers (intermediate steps): let E = 1 V/m, put A and B at x = 0 so V(A)=V(B)=V0. If C is at x = 2 m, V(C) = V0 - (1 V/m)(2 m) = V0 - 2 V, which is lower than V0. Why the correct choice is correct: - It states A and B have equal potential (same x) and C is lower (C is to the right, and potential decreases to the right). That matches the mathematical relation above. Why the other options are incorrect: - Option saying C is higher is reversed: moving with the field lowers potential, not raises it. - Option ranking A > B > C assumes vertical differences change V; they do not in a horizontal uniform field. - Option claiming all three are equal ignores the x-dependence of V; C is at a different x so its potential differs. Therefore the correct statement is: the potential at points A and B are equal, and the potential at point C is lower than the potential at point A. This matches the provided answer.

Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure below. Which statement about the electric potential is true?单项选择题

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