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Understanding Lenz's LawConservation of Energy & Direction of Induced Electromagnetic Fields
Lenz's law, giving the direction of induced electromagnetic fields, is a consequence of the law of conservation of energy.
Oersted discovered in 1820 that electric currents induce magnetic fields. About a decade later Michael Faraday discovered that changing magnetic fields induce electric currents. With Maxwell's brilliant synthesis we know that these effects are caused by the fact that changing electric fields induce magnetic fields and changing magnetic fields induce electric fields. Lenz's LawHeinrich Lenz was a Russian physicist who lived from 1804 to 1865. He discovered a simple way to find the direction of the induced electric currents predicted by Faraday's law. An electric current that is induced by a changing magnetic field will in turn induce its own magnetic field. According to Lenz's law, the induced electric current must be in such a direction that the magnetic field induced by the current opposes the original cause of the induced current. There is a common trap here. The induced magnetic field does not necessarily oppose the original magnetic field as many people tend to think. The original magnetic field does not cause the induced electric current. Rather the change in the magnetic field, or more correctly the magnetic flux, induces the electric current. So the induced magnetic field will oppose the change in the original magnetic field rather than the field itself. If, for example, the original field is decreasing, then the induced magnetic field must be in the same direction as the original field to oppose the decrease. Magnetic flux is a way of measuring the total amount of perpendicular magnetic field passing through an area or a surface. According to Faraday's law an electric current will be induced in a coil of wire when the magnetic flux through the coil changes. This flux can change when the magnetic field changes, when the area of the coil changes, when the source of magnetic field moves, or when the coil moves or rotates. In all these cases the current will be induced in such a direction that it in turn induces a magnetic field that opposes this change in magnetic flux. Lenz's Law and Conservation of EnergyLenz's law is a consequence of the law of conservation of energy. According to the law of conservation of energy the total amount of energy in the universe must remain constant. Energy can be neither created nor destroyed. Hence it is impossible to get free energy from nothing. Think about this experiment similar to Faraday's original experiment. Push a bar magnet through a coil of wire. The moving magnet induces an electric current in the wire, which in turn induces its own magnetic field. According to Lenz's law, the induced magnetic field opposes the cause, which is the moving magnet. Hence the induced magnetic field is in a direction to try to stop the moving magnet. If this were not the case, the induced magnetic field would increase the magnet's velocity and thereby increase its kinetic energy. There is no source for this energy. So if the induced magnetic field helped rather than opposed its cause, conservation of energy would be violated. The connection between Lenz's law and the conservation of energy is a good example of the unity of physics. Many laws stem from a few very fundamental principles. Further ReadingHecht, E., Physics:Algebra/Trig, Brooks/Cole, 1997. Knight, R.D., Physics for Scientists and Engineers with Modern Physics, Pearson, 2004. Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.
The copyright of the article Understanding Lenz's Law in Electricity & Magnetism is owned by Paul A. Heckert. Permission to republish Understanding Lenz's Law in print or online must be granted by the author in writing.
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