CUET · PHYSICS · PYQ PAPER 2023

Two identical circular loops P and Q each of radius R and carrying current I are kept in perpendicular planes such that they have a common centre as shown in figure. The magnitude of the net magnetic field at the common centre is :

A \( \frac{\mu_0 I}{R} \)
B Zero
C \( \frac{2\mu_0 I}{R} \)
D \( \frac{\mu_0 I}{\sqrt{2} R} \)

Verified Solution

Answer & Solution

Correct Answer

(D) \( \frac{\mu_0 I}{\sqrt{2} R} \)

Step-by-step Solution

Detailed explanation

Magnetic field from each loop: \( B_L = \frac{\mu_0 I}{2R} \) Net magnetic field (perpendicular vectors): \( B_{net} = \sqrt{B_L^2 + B_L^2} = \sqrt{2 B_L^2} = B_L \sqrt{2} \) \( B_{net} = \frac{\mu_0 I}{2R} \sqrt{2} = \frac{\mu_0 I}{\sqrt{2} R} \)

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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List-I	List-II
(A) First order reaction	(I) \(\text{C}_{12}\text{H}_{22}\text{O}_{11} + \text{H}_2\text{O} \xrightarrow{\text{H}^+} \text{C}_6\text{H}_{12}\text{O}_6 + \text{C}_6\text{H}_{12}\text{O}_6\)
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