CUET · PHYSICS · PYQ PAPER 2023

Choose the correct statement regarding dependence of electric potential at a point due to an electric dipole:

A depends on the position vector \( \vec{r} \) from the center of the dipole only
B depends on the dipole moment vector \( \vec{p} \) only
C inversely proportional to the distance from the center of the dipole
D inversely proportional to the square of the distance from the center of dipole and depends on the angle between the position vector \( \vec{r} \) and dipole moment vector \( \vec{p} \)

Verified Solution

Answer & Solution

Correct Answer

(D) inversely proportional to the square of the distance from the center of dipole and depends on the angle between the position vector \( \vec{r} \) and dipole moment vector \( \vec{p} \)

Step-by-step Solution

Detailed explanation

The electric potential \((V)\) of a dipole is given by \(V=\frac{1}{4 \pi \epsilon_0} \frac{p \cos \theta}{r^2}\). This shows it is inversely proportional to the square of the distance ( \(r^2\) ) and depends on the angle ( \(\theta\) ) between the position vector and the dipole…

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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