Question

Gauss's law in magnetostatics is expressed as,

• A. \( \oint \vec{B} \cdot d\vec{S} = 0 \)
• B. \( \oint \vec{B} \cdot d\vec{I} = 0 \)
• C. \( \oint \vec{B} \cdot \vec{n} dV = 0 \)
• D. \( \oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}} \)

Hint:

Gauss’s law in magnetostatics states that the net magnetic flux through any closed surface is zero, indicating that magnetic monopoles do not exist.

Answer 1

The Correct Option is A

Step 1: Understanding Gauss's law in magnetostatics.
Gauss’s law in magnetostatics states that the magnetic flux through any closed surface is zero, i.e., the net magnetic field lines entering any closed surface is zero, which can be mathematically written as: \[ \oint \vec{B} \cdot d\vec{S} = 0 \] This implies there are no "magnetic charges," and the magnetic field is always solenoidal (no beginning or end).

Step 2: Conclusion.
Thus, the correct expression for Gauss's law in magnetostatics is option (1). \[ \boxed{(1) \, \oint \vec{B} \cdot d\vec{S} = 0} \]