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Lenz's law states that the direction of theelectric currentinduced in aconductor by a changingmagnetic field is such that the magnetic field created by the induced current opposes changes in the initial magnetic field. It is named after physicistHeinrich Lenz, who formulated it in 1834.[1]
The Induced current is the current generated in a wire due to change inmagnetic flux. An example of the induced current is the current produced in thegenerator which involves rapidly rotating a coil of wire in a magnetic field.
It is aqualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law predicts the direction of many effects inelectromagnetism, such as the direction of voltage induced in aninductor orwire loop by a changing current, or the drag force ofeddy currents exerted on moving objects in the magnetic field.
Lenz's law may be seen as analogous toNewton's third law inclassical mechanics[2][3] andLe Chatelier's principle in chemistry.[4]
Lenz's law states that:
The current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion.
Lenz's law is contained in the rigorous treatment ofFaraday's law of induction (the magnitude of EMF induced in a coil is proportional to the rate of change of the magnetic flux),[5] where it finds expression by the negative sign:
which indicates that the inducedelectromotive force and the rate of change inmagnetic flux have opposite signs.[6]
This means that the direction of theback EMF of an induced field opposes the changing current that is its cause.D.J. Griffiths summarized it as follows:Nature abhors a change in flux.[7]
If a change in the magnetic field of currenti1 induces anotherelectric current,i2, the direction ofi2 is opposite that of the change ini1. If these currents are in two coaxial circular conductorsℓ1 andℓ2 respectively, and both are initially 0, then the currentsi1 andi2 must counter-rotate. The opposing currents will repel each other as a result.
Magnetic fields from strong magnets can create counter-rotating currents in a copper or aluminium pipe. This is shown by dropping the magnet through the pipe. The descent of the magnet inside the pipe is observably slower than when dropped outside the pipe.
When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. The direction of an induced current can be determined using the right-hand rule to show which direction of current flow would create a magnetic field that would oppose the direction of changing flux through the loop.[8] In the examples above, if the flux is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to oppose the change.
In electromagnetism, when charges move alongelectric field lines, work is done on them, whether it involves storing potential energy (negative work) or increasing kinetic energy (positive work).
When net positive work is applied to a chargeq1, it gains speed and momentum. The net work onq1 thereby generates a magnetic field whose strength (in units of magnetic flux density (1tesla = 1 volt-second per square meter)) is proportional to the speed increase ofq1. This magnetic field can interact with a neighboring chargeq2, passing on this momentum to it, and in return,q1 loses momentum.
The chargeq2 can also act onq1 in a similar manner, by which it returns some of the momentum that it received fromq1. This back-and-forth component of momentum contributes to magneticinductance. The closer thatq1 andq2 are, the greater the effect. Whenq2 is inside a conductive medium such as a thick slab made of copper or aluminum, it more readily responds to the force applied to it byq1. The energy ofq1 is not instantly consumed as heat generated by the current ofq2 but is also stored intwo opposing magnetic fields. The energy density of magnetic fields tends to vary with the square of the magnetic field's intensity; however, in the case of magnetically non-linear materials such asferromagnets andsuperconductors, thisrelationship breaks down.
Momentum must be conserved in the process, so ifq1 is pushed in one direction, thenq2 ought to be pushed in the other direction by the same force at the same time. However, the situation becomes more complicated when the finite speed of electromagnetic wave propagation is introduced (seeretarded potential). This means that for a brief period the total momentum of the two charges is not conserved, implying that the difference should be accounted for by momentum in the fields, as asserted byRichard P. Feynman.[9] Famous 19th century electrodynamicistJames Clerk Maxwell called this the "electromagnetic momentum".[10] Yet, such a treatment of fields may be necessary when Lenz's law is applied to opposite charges. It is normally assumed that the charges in question have the same sign. If they do not, such as a proton and an electron, the interaction is different. An electron generating a magnetic field would generate an EMF that causes a proton to accelerate in the same direction as the electron. At first, this might seem to violate the law of conservation of momentum, but such an interaction is seen to conserve momentum if the momentum of electromagnetic fields is taken into account.
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