CUET · PHYSICS · PYQ PAPER 2025

A part of an infinitely long current carrying wire is bent into a circular shape as shown in the diagram. The magnetic field at the centre of the circle is

A \( \frac{\mu_0 I}{2\pi r}(\pi + 1) \) normally inward
B \( \frac{\mu_0 I}{2\pi r}(\pi + 1) \) normally outward
C \( \frac{\mu_0 I}{2\pi r}(\pi - 1) \) normally outward
D \( \frac{\mu_0 I}{2\pi r}(\pi - 1) \) normally inward

Verified Solution

Answer & Solution

Correct Answer

(A) \( \frac{\mu_0 I}{2\pi r}(\pi + 1) \) normally inward

Step-by-step Solution

Detailed explanation

\(B_{straight} = \frac{\mu_0 I}{4\pi r}\) (inward for both straight segments) \(B_{loop} = \frac{\mu_0 I}{2r}\) (inward for circular loop) \(B_{total} = B_{straight\_top} + B_{loop} + B_{straight\_bottom}\)…

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.

Same subject

Match List-I with List-II

List-I	List-II
(A) Power of concave lens	(I) Concave lens
(B) Power gets algebraically added	(II) Refraction of light
(C) Image formation by lens	(III) Negative
(D) Always virtual image	(IV) combination of lenses

Choose the correct answer from the options given below:

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The point at which the tangent to the curve \(y = \sqrt{4x-3} - 1\) has its slope \(\frac{2}{3}\) is:

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Consider the LPP: Max \(Z = 5x + 3y\) subject to \(3x + 5y ≤ 15, 5x + 2y ≤ 10 x ≥ 0, y ≥ 0\)
match List - I with List - II

List-I	List-II
(A) Objective function	(I) \(3x + 5y ≥ 15\)
(B) One constraint	(II) \(x, y ≥ 0\)
(C) Non-negative restrictions	(III) \(Z = 5x + 3y\)
(D) Point (1, 2) does not lie in the region	(IV) \(3x + 5y ≤ 15\)

Choose the correct answert from the option given below :

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