Question

Match List-I with List-II.

Choose the correct answer from the options given below :}

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

Hint:

Always look for the term involving $d/dt$. If it's $d\Phi_B/dt$, it's Faraday. If it's $d\Phi_E/dt$, it's Maxwell's addition to Ampere's law.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Maxwell's equations are a set of four partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, optics, and electric circuits.
Step 3: Detailed Explanation:
- A. \(\oint E \cdot dl = - \frac{d\Phi_B}{dt}\): This relates the induced electromotive force to the rate of change of magnetic flux. This is Faraday's Law (II).
- B. \(\oint B \cdot dl = \mu_0 ( I + \varepsilon_0 \frac{d\Phi_E}{dt} )\): This is the generalization of Ampere's law including displacement current. This is the Ampere-Maxwell Law (III).
- C. \(\iint E \cdot da = \frac{Q_{encl}}{\varepsilon_0}\) (where $Q = \int \rho dv$): This relates electric flux to enclosed charge. This is Gauss's Law of Electrostatics (IV).
- D. \(\oint B \cdot dl = \mu_0 I\) (or \(\iint B \cdot da = 0\)): In the context of the provided list matching, $D$ typically maps to the simplified Ampere's Circuital Law (I).
Step 4: Final Answer:
The correct matching is A-II, B-III, C-IV, D-I.