利用Mathematica 10.3 杰出的符号运算和数值计算能力、卓越的数字绘图功能，研究轴对称磁矢势和磁感线的分布. 先将载流圆线圈的磁矢势A 的计算式表达为椭圆积分、求出磁感应强度B="×A 的表达式和磁感线方程，绘制出形象直观的 磁矢势和磁感线的分布图，修正了现有文献中磁感线分布图的一些缺陷.然后把这种分析方法推广应用到载流密绕有限长圆 柱形螺线管和椭球形线圈中去.

The distributions of the axial symmetry magnetic vector potential and the magnetic induction lines are studied by using Mathematica 10.3. The calculation formula of the magnetic vector potential A of the current carrying circular coil is expressed as the elliptic integral，the magnetic induction intensity B="×A and the magnetic induction line equation are deduced，the distribution maps of the magnetic vector potential and the magnetic induction lines are drawn， some defects of the distribution maps of the magnetic induction lines in the current literature are corrected. Then，the present method is applied to the current carrying tightly wound finite-length cylindrical solenoid and ellipsoidal coil.