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The phenomenon of linear motion of conductor in a magnetic field is commonly found in electric machineries such as, electromagnetic brakes, linear induction motor, electromagnetic flowmeter etc. The design and analysis of the same requires an accurate evaluation of induced currents and the associated reaction magnetic fields. The finite element method is a generally employed numerical technique for this purpose. However, it needs stabilization techniques to provide an accurate solution. In this work, such a stabilization technique is developed for the edge elements. The stability and hence the accuracy is brought in by a suitable representation of the source term. The stability and accuracy of the proposed scheme is first shown analytically and then demonstrated with the help of 2D and 3D simulations. The proposed scheme is parameter-free and it would require a graded regular mesh along the direction of motion.