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| Analytical Solution to Time-Harmonic Electromagnetic Field of Tilted Circular Coil by the Coordinate Transformation Method |
| Lei Yinzhao |
| Beihang University Beijing 100191 China |
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Abstract The analytical solution to time-harmonic electromagnetic field of tilted circular coil in infinite vacuum is solved in this paper. A vector Poisson’s equation of modified magnetic vector potential in infinite vacuum is derived from Maxwell’s equations. According to the similarity of vector Poisson’s equation of the modified magnetic vector potential and that of the steady magnetic field in infinite vacuum, the analytical solution to the time-harmonic electromagnetic field produced by the tilted circular coil is derived from the known analytical solution to the steady magnetic field of the circular coil parallel to rectangular coordinate plane by rotation and translation of rectangular coordinate system. According to the invariable quality of the same physical quantity in different coordinate systems, the derived analytical solution is validated. The proposed method is primary and the presented analytical expression is simple, which can be used to solve the linear electromagnetic field problems of complex shape coils.
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Received: 10 December 2009
Published: 04 March 2014
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2010, Vol. 25 
