Question

Match List I with List II

Choose the correct answer from the options given below:

• A. A-I, B-III, C-IV, D-II
• B. A-III, B-IV, C-I, D-II
• C. A-IV, B-II, C-III, D-I
• D. A-II, B-III, C-IV, D-I

Answer 1

The Correct Option is D

The problem asks to match the laws of electromagnetism (List-I) with their corresponding equations (List-II). These laws are derived from Maxwell’s equations.

Gauss’s Law of Electrostatics states that the total electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space. The corresponding equation is:

\[ \oint \mathbf{E} \cdot d\mathbf{a} = \frac{1}{\epsilon_0} \int \rho dV. \]

This matches D – I.

Faraday’s Law of Electromagnetic Induction states that the electromotive force induced in a closed loop is equal to the negative rate of change of the magnetic flux through the loop. The corresponding equation is:

\[ \oint \mathbf{E} \cdot d\mathbf{l} = - \frac{d}{dt} \int \mathbf{B} \cdot d\mathbf{a}. \]

This matches B – III.

Ampere’s Law (with Maxwell’s correction) relates the line integral of the magnetic field around a closed loop to the current passing through the loop and the displacement current. For steady currents, the corresponding equation is:

\[ \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I. \]

This matches C – IV.

Gauss’s Law for Magnetostatics states that the net magnetic flux through a closed surface is zero, indicating there are no magnetic monopoles. The corresponding equation is:

\[ \oint \mathbf{B} \cdot d\mathbf{a} = 0. \]

This matches A – II.

Final Matching:

A – II, B – III, C – IV, D – I