magnetic field (thing)

Derivation of Magnetic field Boundary Conditions

One of Maxwell's equations state that for a magnetic field B

divB=0

Integrate over volume of interest and using Gauss's law and the equation becomes

INTsc B.ds= 0

where INTsc refers to an area intergration over a closed surface. If this imaginary area incorporates two materials equally, and noting that the magnetic flux ψ is given by

ψ=INTs B.ds

then we can conclude that

ψ₁=ψ₂

where ψ₁,ψ₂ are the magnetic fluxes in material 1 and material 2 respectively

        ..........................................
                                                 
        .              ψ₁                            material 1
                                                  
        --------------------------------
                                           
                         ψ₂                 
                                               material 2
        ..........................................