The flux tube's strength, F , is defined to be the magnetic flux through a surface S intersecting the tube, equal to the surface integral of the magnetic field B ( x ) over S F = ∫ ∫ S B ⋅ ⋅ n ^ ^ d S Since the magnetic field is solenoidal, as defined in Maxwell's equations (specifically Gauss' law for magnetism): ∇ ∇ ⋅ ⋅ B = 0 . the strength is constant at any surface along a flux tube. Under the condition that the cross-sectional area, A , of the flux tube is small enough that the magnetic field is approximately constant, F can be approximated as F ≈ ≈ B A . Therefore, if the cross sectional area of the tube decreases along the tube from A 1 to A 2 , then the magnetic field strength must increase proportionally from B 1 to B 2 in order to satisfy the condition of constant flux F. B 2 B 1 = A 1 A 2