CUET · PHYSICS · PYQ PAPER 2025

The electric field intensity at a distance of 20 cm from the centre of a small conducting sphere is \(1.5 \times 10^3 \text{ N}⋅C^{-1}\) and is directed towards the sphere. The charge on the sphere is:

A + 3.3 nC
B - 6.6 nC
C - 3.3 nC
D 0

Verified Solution

Answer & Solution

Correct Answer

(B) - 6.6 nC

Step-by-step Solution

Detailed explanation

\(q = \frac{Er^2}{k}\) \(q = \frac{(1.5 \times 10^3)(0.20)^2}{9 \times 10^9}\) \(q = 6.67 \times 10^{-9} \text{ C}\) Since the field is directed towards the sphere, the charge is negative. \(q = -6.67 \text{ nC}\)

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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Match List-l with List-ll

List-l (Matrix A)	List-ll (Determinant of adjA)
(A) \(\left[\begin{array}{cc}2 & 1 \\ -1 & 2\end{array}\right]\)	(I) 3
(B) \(\left[\begin{array}{ll}3 & 4 \\ 3 & 6\end{array}\right]\)	(II) 6
(C) \(\left[\begin{array}{cc}3 & 7 \\ -2 & -4\end{array}\right]\)	(III) 5
(D) \(\left[\begin{array}{ll}4 & 3 \\ 3 & 3\end{array}\right]\)	(IV) 2

Choose the correct answer from the options given below :

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The electric field intensity at a distance of 20 cm from the centre of a small conducting sphere is \(1.5 \times 10^3 \text{ N}⋅­­C^{-1}\) and is directed towards the sphere. The charge on the sphere is:

Step-by-step Solution

The electric field intensity at a distance of 20 cm from the centre of a small conducting sphere is \(1.5 \times 10^3 \text{ N}⋅C^{-1}\) and is directed towards the sphere. The charge on the sphere is: