关键词: 梯形面电流元, 毕奥-沙伐尔定律, 磁场, 积分算法, 奇异点, 剖分

Abstract: It is useful to design delicate electric equipment if magnetic field distribution of surface electric current can be obtained accurately.The magnetic field caused by an arbitrary surface electric current with the same coil width can be calculated by a semi-analytic method. The method is as follows: firstly， the total surface electric current is divided into the trapezoidal and curved surface electric current segments， and then each curved surface electric current segment is further fitted by several trapezoidal segments. Numerical method is applied to give the analytical solution or one-dimensional integral for magnetic field caused by all trapezoidal segments. Finally， the magnetic field caused by the total surface electric current can be obtained by the summation of the segment vectors and solutions. However， some singularities can be arise when a trapezoidal segment turns to a right-angled trapezoidal or a rectangular one， the field point is inside the trapezoidal segment or at the top and bottom base lines of the trapezoidal segment， and the four singularities are the vertices of the largest square inside the trapezoid. Fortunately， these singularities can be eliminated by some mathematical transformation.

Key words: trapezoidal surface electric current, Biot-Savart law, magnetic field, integral method, singularity, segmentation