CUET · PHYSICS · PYQ PAPER 2025

Which of the following equations represents the Ampere-Maxwell law?

A \( \oint \mathbf{B} \cdot d\mathbf{A} = 0 \)
B \( \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q}{\epsilon_0} \)
C \( \oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\phi_B}{dt} \)
D \( \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_c + \mu_0 \epsilon_0 \frac{d}{dt}\Phi_E \)

Verified Solution

Answer & Solution

Correct Answer

(D) \( \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_c + \mu_0 \epsilon_0 \frac{d}{dt}\Phi_E \)

Step-by-step Solution

Detailed explanation

The Ampere-Maxwell law describes how magnetic fields are generated by both electric currents and changing electric fields. \(\mu_0 I_c\) : Represents the magnetic field produced by the conduction current (traditional current flow). \(\mu_0 \epsilon_0 \frac{d \Phi_E}{d t}\) :…

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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