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

The given question asks us to match the equations and laws in List-I with the respective laws in List-II. Let's analyze each option step by step:

1. Equation A: \(\oint \vec{E} \cdot d\vec{l} = -\frac{d}{dt} \int \vec{B} \cdot d\vec{a}\) 
   Explanation: This equation represents Faraday's Law of Electromagnetic Induction. It indicates that a change in magnetic flux through a closed loop induces an electromotive force (EMF) along the loop. 
   Match: II
2. Equation B: \(\oint \vec{B} \cdot d\vec{l} = \mu_0 \left( I + \varepsilon_0 \frac{d\phi_E}{dt} \right)\) 
   Explanation: This is known as the Ampere-Maxwell Law. It states that magnetic fields are generated by electric currents and changes in electric fields. 
   Match: III
3. Equation C: \(\oint \vec{E} \cdot d\vec{a} = \frac{1}{\varepsilon_0} \int \rho \, dv\) 
   Explanation: This equation is Gauss's Law of Electrostatics, which relates the electric flux through a closed surface to the charge enclosed by the surface. 
   Match: IV
4. Equation D: \(\oint \vec{B} \cdot d\vec{a} = \mu_0 I\) 
   Explanation: This equation is Ampere's Circuital Law, expressing the relationship between an electric current and the magnetic field it generates. 
   Match: I

Therefore, the correct matching is:

• A-II
• B-III
• C-IV
• D-I

This matches option: A-II, B-III, C-IV, D-I