Statement
The net magnetic flux through any closed surface is zero.
∮ B ⋅ dS = 0Explanation
Magnetic fields are continuous and form closed loops. For any closed surface, the number of magnetic field lines entering the surface is equal to the number leaving it.
If we divide a closed surface into small area elements ΔS, the flux through each element is:
ΔϕB = B ⋅ ΔSAdding the flux through all elements:
ϕB = ∑ B ⋅ ΔS = 0This is different from electrostatics, where the net electric flux depends on the charge enclosed.
Conclusion
Since there are no isolated magnetic poles (monopoles), the net magnetic flux through any closed surface is always zero.
