Question

Let A, B and C be the three points in a uniform electric field $\vec{E}$ as shown. The electric potential is

Choose the correct answer from the options given below:

• A. maximum at point C
• B. maximum at point A
• C. maximum at point B
• D. same at all points A, B and C

Hint:

Think of electric field lines exactly like water flowing down a hill due to gravity. Water flows naturally from high altitude (high potential) to low altitude (low potential). Therefore, the point located furthest upstream against the arrows will always be at the highest potential.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question concerns the relative electrostatic potential values at three separate points (A, B, and C) distributed inside a region with a uniform electric field $\vec{E}$.
Note: Per the standard textbook diagram layout for this question, points are arrayed relative to the directional field arrows, where point B is located furthest upstream (against the direction of the field vectors).

Step 2: Key Formula or Approach:
The fundamental relationship connecting electric field direction and potential gradient is given by:
$$\vec{E} = -\vec{\nabla}V \implies \Delta V = -\int \vec{E} \cdot d\vec{r}$$ This mathematical property establishes that electric field lines always point directly in the direction of the steepest decrease in electric potential.

Step 3: Detailed Explanation:
Because electric field lines point from regions of higher electrical potential toward regions of lower electrical potential, traveling down the field lines reduces potential. Conversely, moving opposite to the direction of the field lines increases potential.
Analyzing the spatial distribution along the axis parallel to the uniform field lines:
Point B is positioned furthest to the left (the origin/source direction of the field lines).
Point A and Point C are positioned further downstream along the direction of the field lines.
Therefore, point B sits at the highest electrical potential state, while points further downstream experience a potential drop.
Thus, the electric potential is maximum at point B.

Step 4: Final Answer:
The electric potential is maximum at point B, which matches option (C).