Step 1: Understanding the Concept:
Maxwell's equations are a set of four fundamental equations governing classical electromagnetism.
Gauss's Law for Magnetism states that the net magnetic flux out of any closed surface is zero, which physically implies the non-existence of magnetic monopoles.
Step 2: Key Formula or Approach:
The integral form of Gauss's Law for magnetism is:
\[ \oint \mathbf{B} \cdot d\mathbf{A} = 0 \]
By applying the Divergence Theorem, this is converted into the differential form:
\[ \nabla \cdot \mathbf{B} = 0 \]
Step 3: Detailed Explanation:
Option (A) is Gauss's Law for Electrostatics (\(\nabla \cdot \mathbf{E} = \rho / \varepsilon_0\)).
Option (C) is Faraday's Law of Induction.
Option (D) is Ampere's Law (without Maxwell's displacement current addition).
Option (B) represents that magnetic field lines form continuous closed loops without any sources or sinks, establishing it as Gauss's Law in Magnetostatics.
Step 4: Final Answer:
The correct equation is \(\nabla \cdot \mathbf{B} = 0\).