JEE Physics 2023 Question with Solution

Given: A matching question on electromagnetic laws and their integral forms.

Find: The correct correspondence between List I and List II.

Using the definitions of the laws:

Gauss's Law of electrostatics

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

So A matches IV.

Faraday's law

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

So B matches I.

Gauss's law of magnetism

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

So C matches II.

Ampere-Maxwell law

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

So D matches III.

Therefore, the correct matching is A-IV, B-I, C-II, D-III.

The solution states "The Correct Option is B", but the worked matching and final answer both give A-IV, B-I, C-II, D-III, which corresponds to option A in the provided options. Hence the defensible correct option is A.

Given: Four named laws and four equations.

Find: Which law corresponds to which integral equation.

Identify each by its characteristic quantity:

1. If the closed surface integral of electric field equals enclosed charge divided by permittivity,

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

it is Gauss's Law in electrostatics.

2. If the closed line integral of electric field is related to time rate of change of magnetic flux,

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

it is Faraday's Law.

3. If the closed surface integral of magnetic field is zero,

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

it is Gauss's Law in magnetism.

4. If the closed line integral of magnetic field depends on conduction current and displacement current,

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

it is Ampere-Maxwell Law.

Hence,

• A $\to$ IV
• B $\to$ I
• C $\to$ II
• D $\to$ III

So the correct option is A.