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Gauss' Law of Magnetostatic Interpretation of Divergence of Magnetic Field-Maxwell's Equations

The magnetic flux through any surface is the surface integral of the normal component of Description: Description: 58311.png, i.e.,
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As it is not possible to have an isolated magnetic pole, magnetic flux lines always close upon themselves. Thus, the total magnetic flux through a closed surface must be zero.
∴ Description: Description: 58296.png
This equation is known as the law of conservation of magnetic flux or the integral form of Gauss’ law of magnetostatic fields.
Applying the divergence theorem, we get
Description: Description: 58288.png
∴  Description: Description: 58277.png

This is known as the differential form of Gauss’ law of magnetostatic fields which shows that magnetostatic fields have no sources or sinks and the magnetic field lines are continuous.

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