A flux tube can be defined passing through any closed, orientable surface S 1 in a vector field F , as the set of all points on the field lines passing through the boundary of S 1 . This set forms a hollow tube. The tube follows the field lines, possibly turning, twisting, and changing its cross sectional size and shape as the field lines converge or diverge. Since no field lines pass through the tube walls there is no flux through the walls of the tube, so all the field lines enter and leave through the end surfaces. Thus a flux tube divides all the field lines into two sets; those passing through the inside of the tube, and those outside. Consider the volume bounded by the tube and any two surfaces S 1 and S 2 intersecting it. If the field F has sources or sinks within the tube the flux out of this volume will be nonzero. However, if the field is divergenceless (solenoidal, div ⁡ ⁡ F = 0 ) then from the divergence theorem the sum of the flux leaving the volume through these two surfaces will be zero, so the flux leaving through S 2 will be equal to the flux entering through S 1 . In other words, the flux within the tube through any surface intersecting the tube is equal, the tube encloses a constant quantity of flux along its length. The strength (magnitude) of the vector field, and the cross sectional area of the tube varies along its length, but the surface integral of the field over any surface spanning the tube is equal.