The net magnetic flux through any closed surface is zero. This statement is based on Gauss’s law for magnetism, which is one of the fundamental principles in electromagnetism. According to Gauss’s law for magnetism, the total magnetic flux passing through a closed surface is always zero.
Mathematically, the magnetic flux (Φ) passing through a closed surface is given by the integral of the magnetic field (B) over the surface:
Φ = ∫ B · dA
where B is the magnetic field vector and dA is an infinitesimal area vector.
For any closed surface, the magnetic field lines entering the surface are balanced by an equal number of field lines exiting the surface. This principle holds regardless of the shape or orientation of the closed surface. As a result, the net magnetic flux passing through the closed surface is always zero.
This property of zero net magnetic flux through a closed surface is a consequence of the absence of magnetic monopoles, which are hypothetical isolated magnetic charges. In contrast to electric fields, which can have sources (positive charges) and sinks (negative charges), magnetic fields always form closed loops and do not have isolated magnetic charges.
It is important to note that while the net magnetic flux through a closed surface is zero, there can still be variations in the magnetic field intensity within the enclosed volume, resulting in non-zero local magnetic flux densities at specific points or regions.