高磁导率楔形体外磁标势的分数阶微积分形式

Fractional calculus form of magnetic scalar potential outside the high permeability wedge

在二维情形下,线电荷与导电楔形体的电势分布可用分数阶导数来表示.本文将电的情形推广到磁中,研究了线磁偶极子磁化高磁导率楔形体后的磁标势,将它的表达式用分数阶导数表示,并使用Ansys仿真软件验证.进一步地,在地球物理中,强磁性对称背斜的顶端附近可近似成楔形体,如果它被均匀地磁场磁化,它的磁标势同样也可以用分数阶微积分表示.这两种情况下的磁标势表达式表明,式中的分数阶微积分因子只与楔形体本身的形状有关,而与外部磁场无关.分数阶微积分阶次取决于楔形体尖端角度,一般不是整数,体现了分数阶微积分的过渡性质.

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.