I've been looking into electromagnet design and there is a certain principle/set of equations that are bothering me... (1) B = (kμ0Ni)/L (2) ø = BA Where; - ø = total magnetic flux (wb) - B = magnetic flux density (wb/m2) I am trying to solve for an optimum cross sectional area of core material in a solenoid, however according to these equations flux density (field strength) is not proportional to cross sectional area. So in theory you could keep increasing the diameter of your core material to increase the total flux with all other variables staying constant. I would have thought that total flux was a conserved quantity with flux density reducing with increased area. This does not seem to be the case, and makes little sense. As a physical analogy, it seems like having a material of constant density and increasing the volume to increase the mass... breaking every rule in the book! I may well be missing something somewhere along the way, if you could advise as to a solution to my cross sectional 'core area' problem that'd be great.