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: Gauss's Law for Magnetism Explained.
Gauss's law for magnetism asserts that the total magnetic flux through any closed surface is zero. This signifies that the number of magnetic field lines entering a closed surface equals the number exiting, expressed mathematically as: \[\oint \vec{B} \cdot d\vec{S} = 0\] This indicates the absence of magnetic monopoles; magnetic fields are always solenoidal, possessing no source or sink.

Step 2: Final Statement.
Therefore, option (1) accurately represents Gauss's law in magnetostatics. \[\boxed{(1) \, \oint \vec{B} \cdot d\vec{S} = 0}\]