Match List I and List II
A. Gauss's Law in Electrostatics        I. $$\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$$
B. Faraday's Law                          II. $$\oint \vec{B} \cdot d\vec{A} = 0$$
C. Gauss's Law in Magnetism        III. $$\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$$
D. Ampere-Maxwell Law          IV. $$\oint \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0}$$
Choose the correct answer from the options given below :

Solution :

Gauss’s Law in Electrostatics relates electric flux through a closed surface to the enclosed charge :

$$\oint \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0}$$

Hence,

A → IV

Faraday’s Law states that induced emf is equal to the negative rate of change of magnetic flux :

$$\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$$

Hence,

B → I

Gauss’s Law in Magnetism states that net magnetic flux through a closed surface is zero :

$$\oint \vec{B} \cdot d\vec{A} = 0$$

Hence,

C → II

Ampere-Maxwell Law relates magnetic field with conduction current and changing electric flux :

$$\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$$

Hence,

D → III

Final Answer :

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