矢量法求解矩形电流激发的磁场空间分布

Magnetic Field Distribution of Rectangle Coil by Vector Method

磁感应强度是电磁学中重要的物理矢量,运用矢量运算方法求解磁场,可提高学生解决物理问题的能力和空间想象力,对学生学好物理、用好物理规律具有重要的意义。用矢量运算,求得矩形电流线圈激发的磁场在空间分布的精确解,形象地表明了在导线所在位置处,存在奇点;在线圈平面内,中间的磁场小,靠近线圈导线的磁场大;导线二侧的磁场方向相反;线圈外侧磁场,随距离的增大,很快趋于零;在矩形线圈二导线交点处的磁场大于等距离的它处;在线圈平面附近,z方向的磁场大,x,y方向的磁场小;线圈内的磁场大于线圈外的磁场;磁场方向遵循右手螺旋定则。

Electric field and magnetic field are two important physical vectors in electromagnetics. It has important meanings that students enhance the ability using vector operation to solve physics problems. This paper applies vector method to obtain the exact solution for space distribution of magnetic field excited by rectangle coil. The plots show that there exists singularity in the coil position; in the coil plane,the middle magnetic field is small but big near wire; the magnetic field possesses opposite direction at the two sides of coil; the outside magnetic field tends quickly to zero with the increasing distance; at the intersection points of two coils,the magnetic field is greater than the other equidistance; near the coil plane,the magnetic field in z direction is big but small along x and y; the magnetic field within the coil is greater than outer; and the magnetic field direction follows the right-hand screw rule.