柱坐标下毕奥-萨伐尔定律及其应用OA
由毕奥-萨伐尔定律的微分形式出发,详细推导柱坐标系下的毕奥-萨伐尔定律形式,并利用该形式计算有限长载流直导线,载流圆线圈,无限长载流圆柱面等具有轴对称性的载流导线在空间中产生的磁场分布.结果发现,对于具有轴对称性的载流导线,用柱坐标系下的毕奥-萨伐尔定律形式求解其磁场的分布会更加方便.特别是在计算载流圆线圈在空间任一点产生的磁场方面,仅需计算磁场的径向和角向 2 个分量的积分即可得到最终结果.
Beginning with the differential form of the Biot-Savart law,the expression of the Biot-Savart law in cylindrical coordinates is derived in detail,and this form is used to calculate the magnetic field distribution in space generated by axisymmetric current-carrying wires such as finite length straight wires,current-carrying circular coils,and infinitely long current-carrying cylinders.The results demonstrate that the cylindrical coordinate representation of the Biot-Savart law offers greater convenience for determining magnetic fields produced by axially symmetric current conductors.Notably,in calculating the magnetic field generated by a current-carrying circular coil at any point in space,the final result can be obtained by only calculating the integral of the radial and angular components of the magnetic field.
王伟懿;何玲逸;李瑶;夏继豪;李子良
中国矿业大学(北京),北京 100083中国矿业大学(北京),北京 100083中国矿业大学(北京),北京 100083中国矿业大学(北京),北京 100083中国矿业大学(北京),北京 100083
数理科学
毕奥-萨伐尔定律柱坐标轴对称载流圆线圈载流圆柱面
Biot-Savart lawcylindrical coordinateaxial symmetrycurrent-carrying circular coilcurrent-carrying cylinder
《科技创新与应用》 2026 (3)
9-12,4
中国矿业大学(北京)教学改革项目(J2507)中国矿业大学(北京)大学生创新训练项目(202407008)
评论