A uniform electric field is prevalling on X - direction in certain region. The co-ordinates of points P , Q and R are (0,0),(2,0) and (0,2) respectively. Which of the following alternatives is true for the potentials at these points?

A \(V _{ P }= V _{ Q }, V _{ Q }> V _{ R }\)
B \(V _{ P }= V _{ Q }, V _{ P }> V _{ R }\)
C \(V _{ P }= V _{ R }, V _{ P }> V _{ Q }\)
D \(V _{ P }= V _{ Q }, V _{ P }> V _{ R }\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(V _{ P }= V _{ R }, V _{ P }> V _{ Q }\)

Step-by-step Solution

Detailed explanation

For a point on a plane perpendicular to the electric field, the electric potential is the same.
\(\therefore V _{ P }= V _{ R }\) (equipotential surface)
The potential decreases in the direction of the uniform electric field.
\(\therefore V _{ P }> V _{ Q }\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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