Which of the following option gives correct equation for Gauss' Law of magnetism?

  1. \(\oint \overrightarrow{E}.\overrightarrow{dA}= {q\over {\epsilon_0}}\)
  2. \(\oint \overrightarrow{E}.\overrightarrow{dA}= 0\)
  3. \(\oint \overrightarrow{B}.\overrightarrow{dA}=0\)
  4. None of the above

Answer (Detailed Solution Below)

Option 3 : \(\oint \overrightarrow{B}.\overrightarrow{dA}=0\)
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Detailed Solution

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CONCEPT:

  • Gauss's law for magnetism is one of the four of Maxwell's equations.
  • It states that the magnetic field B has divergence equal to zero.

The integral form of Gauss's law for magnetism states:

\(\oint \overrightarrow{B}.\overrightarrow{dA}=0\)

where B is the magnetic field and dA is any closed surface vector whose magnitude is the area of an infinitesimal piece of the surface, and whose direction is the outward-pointing surface normal.

  • Gauss's law for magnetism states that magnetic flux through a closed surface is always zero.

EXPLANATION:

Magnetic flux through a closed surface is given by: 

\(\phi = \oint \overrightarrow{B}.\overrightarrow{dA}\)

and Gauss's law for magnetism states that magnetic flux through a closed surface is always zero.

\(\oint \overrightarrow{B}.\overrightarrow{dA}=0\)

So the correct answer is option 3.

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