Question

	LIST I		LIST II
A.	∇ ⋅ E = ρ/ε₀		I. Gauss's Law in magnetostatics
B.	∇ ⋅ B = 0		II. Faraday's Law of electromagnetic Induction
C.	∇ × E = - ∂B/∂t		III. Gauss's Law in electrostatics
D.	∇ × B = μ₀J + μ₀ε₀ ∂E/∂t		IV. Modified Ampere's Law

Choose the correct answer from the options given below:

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

Hint:

Maxwell’s equations describe the behavior of electric and magnetic fields in both static and dynamic situations. The correct match of the equations is important for understanding electromagnetism.

Answer 1

The Correct Option is B

\( \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} \) is Gauss's Law in electrostatics (A).
\( \nabla \cdot \mathbf{B} = 0 \) is Gauss's Law in magnetostatics (B).
\( \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \) is Faraday's Law (C).
\( \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \) is the Modified Ampere's Law (D)