Question

If B is magnetic field and q is the charge then the following represents the Gauss's law of magnetism

• A. $\displaystyle \oint \vec{B} \cdot d\vec{S} = 0$
• B. $\displaystyle \oint \vec{B} \cdot d\vec{S} = q$
• C. $\displaystyle \oint \vec{B} \cdot d\vec{S} = 4\pi$
• D. $\displaystyle \oint \vec{B} \cdot d\vec{S} = \mu_0 q$

Hint:

Maxwell's 2nd Equation (Gauss's Law for Magnetism):

• Net magnetic flux through any closed surface is zero.
• This supports the non-existence of magnetic monopoles.
• Equation: $\oint \vecB \cdot d\vecS = 0$.
• Do not confuse with Gauss’s law for electric field: $\oint \vecE \cdot d\vecS = \fracq\varepsilon_0$.

Answer 1

The Correct Option is A

Gauss’s law for magnetism is one of Maxwell’s four fundamental equations. It states that the total magnetic flux through a closed surface is always zero: \[ \oint \vec{B} \cdot d\vec{S} = 0 \] This means there are no magnetic monopoles in nature—unlike electric charges, we cannot isolate a single north or south magnetic pole. Magnetic field lines always form closed loops, entering and exiting any closed surface equally. Since no net flux is produced, the integral evaluates to zero. Therefore, the correct representation of Gauss's law for magnetism is option (1).

Answer 2

Step 1: Understand Gauss's law for magnetism
Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero.
This implies there are no magnetic monopoles; magnetic field lines are continuous and always form closed loops.

Step 2: Express the law mathematically
The magnetic flux \( \Phi_B \) through a closed surface \( S \) is given by the surface integral:
\[ \Phi_B = \oint \vec{B} \cdot d\vec{S} \]
where \( \vec{B} \) is the magnetic field and \( d\vec{S} \) is the infinitesimal area vector on surface \( S \).

Step 3: Statement of Gauss's law for magnetism
According to Gauss's law for magnetism:
\[ \oint \vec{B} \cdot d\vec{S} = 0 \]
which means the total magnetic flux through any closed surface is zero.

Step 4: Conclusion
Thus, the correct mathematical representation of Gauss's law for magnetism is:
\[ \boxed{\oint \vec{B} \cdot d\vec{S} = 0} \]