物理实验论文单线圈产生的三维磁场的理论推导与测试

东南大学物理实验课程论文

2013大学生物理实验研究论文

单线圈产生的三维磁场的理论推导与测试

(东南大学 南京 210000)

摘 要: 本文旨在将大学物理实验的利用霍尔效应测量单个载流圆线圈轴线上磁感应强度一节从一维拓展到三维。据此,本文先在球坐标系下利用磁感应强度的计算公式毕奥-萨伐尔定律以及单个载流圆线圈产生磁场的对称性推导出了全空间任意一点的磁感应强度,然后借助实验室DH4501N型三维亥姆霍兹线圈磁场实验仪对其进行了测试验证。发现实验测定的结果和理论值二者吻合的相当好,验证了推导的正确性。 关键词: 单个载流圆线圈;磁感应强度;三维

Theoretical Analysis and Testing of Three - Dimensional Magnetic Field Generated by a Single

Coil

(Southeast University Nan Jing 210000)

Abstract: This article aimed to extend the college physics experiment which uses Hall effect to measure the magnetic induction

on the axis of a single current-carrying round coil from a one-dimensional to three – dimensional, Accordingly , the first is taking advantage of magnetic induction strength formula Biot - Savart law and the symmetry of a magnetic field which is generated by a single current-carrying round coil to deduce the magnetic induction at any point of the whole space in a spherical coordinate system. Then, with the help of the DH4501N three-dimensional Helmholtz coil magnetic field experimental apparatus in the laboratory, the author carried out testing and validation. Finally, the author discoveries that the experimental measurement results and the theoretical value agree with each other quite well, which verifies that the derivation is correct. key words: a single current-carrying round coil; magnetic induction; three – dimensional

大学物理实验在利用霍尔效应测量单个载流圆线圈的磁场时,只要求测量了圆线圈轴线上(即Z轴)的磁感应强度并进行绘图,只停留在一维角度。

而本文利用毕奥萨伐尔定律推导了全空间任意一点的磁感应强度的理论公式,然后利用实验室的DH4501N型三维亥姆霍兹线圈磁场实验仪进行了相关验证,发现实验结果和理论值符合得很好,验证了

推导的正确性,从而成功地将单个载流圆线圈产生的磁场验证从一维扩展到了三维。

1 推导空间任一点P的矢势A

假设已知载流圆线圈的圆心为O, 半径为R , 电流强度为I ,目的是计算该载流圆线圈平面内任一点P 的磁感应强度B。

物理实验论文单线圈产生的三维磁场的理论推导与测试

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