Question

The Gauss's law for magnetic fields is

• A. \(\nabla \cdot E = 0\)
• B. \(\nabla \cdot H = 0\)
• C. \(\nabla \cdot B = 0\)
• D. \(\nabla \cdot D = 0\)

Hint:

Gauss's law for electricity: \[ \nabla \cdot D=\rho_v \] Gauss's law for magnetism: \[ \nabla \cdot B=0 \]

Answer 1

The Correct Option is C

Concept: Gauss's law for magnetism is one of Maxwell's equations. It states that magnetic monopoles do not exist and hence the net magnetic flux through any closed surface is zero. \[ \oint_S \vec{B}\cdot d\vec{S}=0 \] The differential form is \[ \nabla \cdot \vec{B}=0 \]

Step 1: Recall Maxwell's equation for magnetic fields.
The divergence of magnetic flux density is always zero. \[ \nabla \cdot B = 0 \]

Step 2: Interpret the physical meaning.
Since isolated magnetic charges do not exist, magnetic field lines always form closed loops. Therefore, the net magnetic flux leaving a closed surface is zero.

Step 3: Final Answer.
\[ \boxed{\nabla \cdot B = 0} \] Hence, \[ \boxed{\text{Correct Option (C)}} \]