Fractional calculus form of magnetic scalar potential outside the high permeability wedge
In a two-dimensional case,the potential of line charge and conductive wedges can be represented by fractional derivatives.This article extends the case of electricity to magnetism and studies the magnetic scalar potential of a high permeability wedge magnetized by a linear magnetic dipole.The expression containing fractional derivative factors is derived and then verified using Ansys simulation software.Furthermore,in geophysics,the vicinity of the top of a magnetic symmetric anticline can be approximated as a wedge.If it is magnetized by a uniform magnetic field,its magnetic scalar potential can also be expressed by fractional calculus.The magnetic scalar potential expressions in these two cases indicate that the fractional calculus in the equation is only related to the shape of the wedge itself,and is independent of the external magnetic field.The order of fractional calculus depends on the angle of the wedge tip and is generally not an integer,reflecting the transitional properties of fractional calculus.
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