A field of force created by and acting on moving charges (ie current). In reality the magnetic field is only one facet of the electromagnetic field which is caused by moiving and stationary charges according to Maxwell's equations and acts on all charged particles according to the Lorentz force law.

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
ψ12
where ψ12 are the magnetic fluxes in material 1 and material 2 respectively

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

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