Electromagnetic Induction Bo Zhou Faculty of Science, Hokudai
Oersted's law Oersted s discovery in 1820 that there was a close connection between electricity and magnetism was very exciting until then, the two subjects had been considered as quite independent. Oersted noticed that the needle of a compass next to a wire carrying current turned so that the needle was perpendicular to the wire. From Wikipedia
Induced Currents Move a bar magnet in the presence of a circuit consisting of a wire coil and an ammeter. Electromagnetic induction was discovered independently by Michael Faraday in 1831 and Joseph Henry in 1832.
Magnetic Flux We have known that the magnetic flux through any closed surface is zero. Here we re interested in the flux through open surfaces, which need not be zero. magnetic flux is the integral of the magnetic field over a surface
Quiz A solenoid of circular cross section has radius R, consists of n turns per unit length, and carries current I. Find the magnetic flux through each turn of the solenoid.
Quiz A long, straight wire carries current I. A rectangular wire loop of dimensions l by w lies in a plane containing the wire, with its closest edge a distance a from the wire and its dimension l parallel to the wire. Find the magnetic flux through the loop.
Faraday s law of induction The induced emf in a circuit is proportional to the rate of change of magnetic flux through any surface bounded by that circuit. εε = ddφ BB dddd (Faraday s law) Where εε is the induced emf in a circuit and Φ BB is the magnetic flux through any surface bounded by that circuit. Faraday s law relates the induced emf to the change in flux. It isn t magnetic field or flux that causes an induced emf it s the change in flux.
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Lenz's Law Move a bar magnet toward a wire loop. An induced current flows, dissipating energy as it heats the loop. Where did that energy come from? What s the direction of the induced current? Conservation of energy determines the direction of the induced current.
Lenz's Law The direction of an induced emf or current is such that the magnetic field created by the induced current opposes the change in magnetic flux that created the current. [Lenz s Law] Mathematically, Lenz s law is contained in the minus sign that appears in Faraday s law, but it s usually easier to use Faraday s law to find the magnitude of the induced emf and then reason out the direction using energy conservation. A circular coil in a decreasing magnetic field.
"magnet drop" experiment A common experiment demonstrating Lenz's law is the "magnet drop" experiment. In this experiment, a (often powerful, neodymium) magnet is dropped through a conducting tube, often made of copper. The changing magnetic flux as the magnet falls induces a current in the tube which creates a magnetic field opposing the magnetic field of the permanent magnet. Because like poles of a magnet repel and the induced magnetic field appears to be a like pole at either end of the magnet, a magnetic force is exerted on the permanent magnet that slows its fall due to gravity. https://brilliant.org/wiki/lenzs-law/
Motional emf and Lenz s Law Consider a conducting bar of length l moving through a uniform magnetic field which points into the page. What will happen? What s the electric power produced? PP = BB2 ll 2 vv 2 RR
Electric Generators One of the most important applications of Faraday s law is to generators and motors. A generator converts mechanical energy into electric energy, while a motor converts electrical energy into mechanical energy. N turns in the loop What s the current generated in the circuit?
Electric Generators Electromagnetic induction is also the basis of magnetic recording, once the dominant means of storing audio, video, and computer information but now more common in credit cards and similar applications
Inductance There are many ways to change magnetic flux and thus induce emfs and currents. We can move a magnet, or move or rotate the circuit. self-inductance
Induced Electric Fields What causes the emf in a conducting loop subject to a changing magnetic field? There s no motion, yet there must be a force on the free charges in the conductor. There must be an electric field an induced electric field in the conducting loop. A changing magnetic field creates an electric field.
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Quiz A bar magnet moving toward a current loop. Determination of the direction of induced current by considering the magnetic force between the bar magnet and the loop
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