CUET · PHYSICS · PYQ PAPER 2023

Equipotential surfaces at a great distance from a collection of charges whose total sum is not zero are approximately:

A Spherical
B Planes
C Paraboloidal
D Ellipsoidal

Verified Solution

Answer & Solution

Correct Answer

(A) Spherical

Step-by-step Solution

Detailed explanation

At a distance much larger than the spread of the charges, the entire collection behaves like a single point charge. Since the equipotential surfaces for a point charge are surfaces of constant radius, they form concentric spheres. A) Spherical

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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From CUET

Match List - I with List - II.

LIST I Differential equation	LIST II Integrating Factor (I.F)
A. \(\frac{d y}{d x}-\frac{y}{x}=2 x\)	I. \(x^2-1\)
B. \(\frac{d y}{d x}+\left(\frac{2 x}{x^2-1}\right) y=\frac{2}{\left(x^2-1\right)^2}\)	II. \(\sqrt{1-x^2}\)
C. \(\frac{d y}{d x}-\left(\frac{x}{1-x^2}\right) y=\frac{1}{1-x^2}\)	III. \(\frac{1}{x}\)
D. \(\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{\cot x}{1+x^2}\)	IV. \(1+x^2\)

Choose the correct answer from the options given below:

CUET 2023 Hard

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List-I (Formula)	List-II (Physical quantity)
(A) \( neAv_d \)	(I) Mobility
(B) \(\frac{v_d}{E}\)	(II) Current
(C) \(\frac{n e^2 \tau}{m}\)	(III) Conductivity
(D) \(\frac{m}{n e^2 \tau}\)	(IV) Resistivity