An electric field is spread uniformly in Y axis. Consider point A as origin point. The co-ordinates of point B are equal to (0,2) m. The co-ordinates of point C are (2,0) m. At points A, B and C electric potentials are \(V_A, V_B\) and \(V_C\) respectively. From the following options which is correct ?

A \(V _{ A }= V _{ C }< V _{ B }\)
B \(V_A=V_B=V_C\)
C \(V_A=V_B>V_C\)
D \(V_A=V_C>V_B\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(V_A=V_C>V_B\)

Step-by-step Solution

Detailed explanation

(D)

For a point (A and C ) on a plane perpendicular to the electric field, the electric potential is the same.
\(\therefore V_{A}=V_{C}\)
The potential decreases in the direction of uniform electric field.
\(\therefore V_{A}>V_{B} \text { and } V_{C}>V_{B}\)

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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