Magnetic-field lines form continuous loops: they do not begin or end on isolated magnetic charges. Gauss's law for magnetism expresses this by stating that the net magnetic flux through every closed surface is zero:

$$\oint_S\mathbf B\cdot d\mathbf A=0.$$

Meaning of zero net flux

Magnetic field can certainly pass through a closed surface. The law says that the total outward flux equals the total inward flux.

A bar magnet placed inside a closed surface, for example, produces field leaving some parts of the surface and entering others, but the signed contributions cancel.

No observed magnetic monopoles

Electric Gauss's law relates net electric flux to enclosed electric charge. The magnetic law has no corresponding magnetic-charge term because isolated magnetic monopoles have not been observed in classical electromagnetism.

Cutting a bar magnet in half therefore produces two smaller dipole magnets rather than separate north and south magnetic charges.

The local differential form of this law appears later together with the other Maxwell equations, once the required vector-calculus language is available.