Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 34. Electromagnetic Induction Electromagnetic induction is the scientific principle that underlies many modern technologies, from the generation of electricity to communications and data storage. Chapter Goal: To understand and apply electromagnetic induction.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic Induction If a magnet is moved towards a circuit, or a circuit moved towards a magnet, a current is induced in the circuit. The direction of the current is such that its field opposes the inducing field (Lenz’s rule)Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic Induction In the case of a stationary circuit, the induced current is driven by an electric field associated with the changing magnetic field. The “electromotive force” an be observed with a voltmeter. Whenever a magnetic field is changing, a new sort of circulating electric field exists.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic data storage encodes information in a pattern of alternating magnetic fields. When these fields move past a small pick-up coil, the changing magnetic field implies an electric field which induces current in the coil. The current pulses represent the 0s and 1s of digital data. Magnetic Induction ApplicationCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic induction can be used to sense the positions of ferromagnetic steel strings in a guitar. In this application, the motion of magnetized strings implies time dependent magnetic and hence electric fields. Magnetic Induction ApplicationCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Motional magnetic induction In the case in which the circuit moves, the electromotive force is the magnetic force on the electrons forced to move moving with the circuit. These effects are related – they are the same effect viewed in different frames of reference.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Motional magnetic example The magnetic motional EMF in this sliding bar circuit is the integral of the magnetic force per unit charge F/q=vB along the length l of the bar.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.1 Measuring the earth’s magnetic fieldCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.1 Measuring the earth’s magnetic fieldCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electric generator The loop rotation (driven by human or water or steam power) moves wires in a fixed B field generating an EMF by motional induction. Mechanical energy is converted to electrical energy.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Eddy currents B B Motional induction produces currents and braking forces when a conductor moves in a magnetic field.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Faraday’s Law dS B B The EMF in any closed loop is the negative of the time rate of change of magnetic flux through any closed surface spanning the loop: Direction of flux related to direction of EMF by r.h. rule. The 2nd form applies to motional EMF also.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Alternating voltage/currentCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electric motors The generator may be run in reverse. If an alternating current is caused to flow in the loop, the magnetic force on the wires causes the loop to rotate. Electrical energy is converted to mechanical energy.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s generalization of Faraday’s LawCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s Equations Not only charges produce E-field a changing B-field also produces an E-field Not only currents produce B-field a changing E-field produces a B-field E • ds∫= 0 becomes E • ds∫= 0 − dΦBdt B • ds∫=µoI becomes B • ds∫=µoI +µoεodΦEdt ⇒ E ≠ −∇VCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s Equations Gauss’s Law No magnetic monopoles Faraday’s Law Ampere’s LawCopyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s Equations The part of E that diverges comes from charge No part of B diverges A part of E circulates associated with time dependent B The circulation of B comes from I and also is associated with time dependent E.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electromagnetic waves Maxwell discovered there are self sustaining wave solutions in the absence of charge and current, transverse waves that move at light speed.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic inductance in circuits A current in one circuit generates a magnetic field and magnetic flux in another circuit. A change in the current implies a change in magnetic field and linked flux and an associated electric field, an EMF, and an induced current in the other circuit. The flux in one circuit j due to one ampere in another I is a geometric quantity called the mutual inductance Lij. The flux in a single circuit due to its own magnetic field is called its self inductance L=Lii.Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic inductance defined B I1 I2Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Self inductance of a coil Prototype: The self inductance of a solenoid having N turns, length l and cross-section area A is the flux for N turns N*B*A per unit current for which B = mu0 NI/l = mu0 N/l: In changing the current in a circuit, the induced EMF opposes the increase in current. If the rate of change is fast enough, these induced EMFs can be as important as any static voltage source!Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.12 The length of an inductorCopyright © 2008 Pearson Education, Inc., publishing as Pearson
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