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The objective of this paper is to discuss the use of the null field integral equations in the solution of eddy current magnetic field problems. Their usage is approached through a development of the "classical" boundary integral equation technique as applied to irregularly shaped two-dimensional objects. Two immediate advantages are discussed, the first being the circumvention of singularities in the integrands. The second is the ability to improve the conditioning of the determination matrix by appropriate choice of null field points. The technique is tested on an irregularly shaped ellipsoid and results compared to those obtained from perturbation theory.