CUET · PHYSICS · PYQ PAPER 2023

A conducting sphere of radius R is given a charge Q. What is the electric field and the electric potential at the centre of the sphere?

A \( \frac{Q}{4\pi\epsilon_0 R^2} \) and \( \frac{Q}{4\pi\epsilon_0 R} \)
B \( \frac{Q}{4\pi\epsilon_0 R^2} \) and zero
C zero and \( \frac{Q}{4\pi\epsilon_0 R} \)
D Both electric field and electric potential are zero

Verified Solution

Answer & Solution

Correct Answer

(C) zero and \( \frac{Q}{4\pi\epsilon_0 R} \)

Step-by-step Solution

Detailed explanation

Electric field at center: \( 0 \) Electric potential at center: \( \frac{Q}{4\pi\epsilon_0 R} \)

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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