Lenz's law
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Lenz's law states that the direction of the
It is a qualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law predicts the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductor or wire loop by a changing current, or the drag force of eddy currents exerted on moving objects in a magnetic field.
Lenz's law may be seen as analogous to Newton's third law in classical mechanics[2][3] and Le Chatelier's principle in chemistry.[4]
Definition
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 of Faraday'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 induced electromotive force and the rate of change in magnetic flux have opposite signs.[6]
This means that the direction of the
If a change in the magnetic field of current i1 induces another electric current, i2, the direction of i2 is opposite that of the change in i1. If these currents are in two coaxial circular conductors ℓ1 and ℓ2 respectively, and both are initially 0, then the currents i1 and i2 must counter-rotate. The opposing currents will repel each other as a result.
Example
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.
Detailed interaction of charges in these currents
In electromagnetism, when charges move along electric 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 charge q1, it gains speed and momentum. The net work on q1 thereby generates a magnetic field whose strength (in units of magnetic flux density (1 tesla = 1 volt-second per square meter)) is proportional to the speed increase of q1. This magnetic field can interact with a neighboring charge q2, passing on this momentum to it, and in return, q1 loses momentum.
The charge q2 can also act on q1 in a similar manner, by which it returns some of the momentum that it received from q1. This back-and-forth component of momentum contributes to magnetic
Conservation of momentum
Momentum must be conserved in the process, so if q1 is pushed in one direction, then q2 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 (see
References
- ^ Lenz, E. (1834), "Ueber die Bestimmung der Richtung der durch elektodynamische Vertheilung erregten galvanischen Ströme", Annalen der Physik und Chemie, 107 (31), pp. 483–494. A partial translation of the paper is available in Magie, W. M. (1963), A Source Book in Physics, Harvard: Cambridge MA, pp. 511–513.
- ^ Schmitt, Ron. Electromagnetics explained. 2002. Retrieved 16 July 2010.
- ISBN 9781135071134.
- .
- ^ "Faraday's law of electromagnetic induction". 26 February 2021. Retrieved 2021-02-27.
- ^ Giancoli, Douglas C. (1998). Physics: principles with applications (5th ed.). pp. 624.
- ISBN 978-0-321-85656-2.
- ^ "Faraday's law and Lenz's law". buphy.bu.edu. Retrieved 2021-01-15.
- ^ The Feynman Lectures on Physics: Volume I, Chapter 10, page 9.
- ^ Maxwell, James C. A treatise on electricity and magnetism, Volume 2. Retrieved 16 July 2010.
External links
- Media related to Lenz's law at Wikimedia Commons
- A dramatic demonstration of the effect on MRI