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Abstract This paper reviews the analytical methods for electromagnetic fields.Firstly,the importance of analytical solutions is pointed out,i.e.analytical solutions reveal the variation law of electromagnetic fields visually;there is no numerical instability;expressions can be derived repeatedly by others and their form is full of scientific beauty;they are the foundation of numerical solutions and widely used as calculation formulas to solve engineering problems.Secondly,several frequently-used analytical methods are introduced,such as the method of separation of variables,the complex variable function method,the Green function method,the integral transform method,and the approximate analytical method.Furthermore,some classical analytical solutions are reviewed,including the Lampard-Thompson theorem,the van der Pauw formula,the expression of the uniform magnetic field in the central zone of a solenoid coil,the analytical solution to the impedance variation of a probe coil above a conductive plate,calculation method for the magnetic field of the Halbach permanent-magnet,the standard calculation formula of the brain magnetic measurement,the three-dimensional asymptotic analytical solution to the eddy current field of a conductive plate with shallow surface defect,and the three-dimensional analytical solution to the eddy current field of a metal pipe.What's more,several reference books are selectively introduced to find analytical solutions.Finally,a number of problems are proposed for further study,containing applying conformal mapping method in solving problems of static magnetic field,integrating existing analytical methods,introducing latest methods of mathematical physics,analytically solving the transient eddy current field,deducing higher order derivative terms of the field quantity in the perturbation method,and analytically solving inverse problems.
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Received: 01 July 2016
Published: 02 November 2016
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2016, Vol. 31 
