Resolving a paradox in the teaching of faraday's law / | |
Autor: | David Wunsch, A. |
Tema(s): | |
Resumen: | In the classroom development of Faraday's law and its application to transformers, one inevitably obtains a paradox: The magnetic field outside the transformer's core is assumed to be zero in the calculation, while the electric field outside the core must be nonzero if a voltage is to appear in the transformer's secondary. This electromagnetic field external to the core violates Maxwell's equations. We resolve this paradox by finding both the electric and magnetic fields, and using a line integration of the electric field to obtain the voltage in the secondary. We show it to be nearly identical to the result obtained by the traditional application of Faraday's law of induction, based on changing flux in the transformer's core. Justification for the traditional approach is provided. The discussion is of a level typically seen in graduate-level courses, and can provide a good example and challenge for computing the electric fields using vector potentials. With guidance, this paper could also be comprehensible to undergraduates in electromagnetic engineering, particulary those in two-semesters EM courses who spend significant time on the elementary integral equations |
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In the classroom development of Faraday's law and its application to transformers, one inevitably obtains a paradox: The magnetic field outside the transformer's core is assumed to be zero in the calculation, while the electric field outside the core must be nonzero if a voltage is to appear in the transformer's secondary. This electromagnetic field external to the core violates Maxwell's equations. We resolve this paradox by finding both the electric and magnetic fields, and using a line integration of the electric field to obtain the voltage in the secondary. We show it to be nearly identical to the result obtained by the traditional application of Faraday's law of induction, based on changing flux in the transformer's core. Justification for the traditional approach is provided. The discussion is of a level typically seen in graduate-level courses, and can provide a good example and challenge for computing the electric fields using vector potentials. With guidance, this paper could also be comprehensible to undergraduates in electromagnetic engineering, particulary those in two-semesters EM courses who spend significant time on the elementary integral equations
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