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Electromagnetic Induction Ch. 29 Induction experiments Faraday’s law Lenz’s law Motional electromotive force Induced electric fields Displacement Current C 2009 J. Becker (sec. 29.1) (sec. 29.2) (sec. 29.3) (sec. 29.4) (sec. 29.5) (sec. 29.7) Current induced in a coil. When B is constant and shape, location, and orientation of coil does not change, the induced current is zero. Conducting loop in increasing B field. Magnetic flux through an area. Lenz’s Law: The induced emf or current always tends to oppose or cancel the change that caused it. Lenz’s law Faraday’s Law of Induction How electric generators, credit card readers, and transformers work. A changing magnetic flux causes (induces) an emf in a conducting loop. C 2004 Pearson Education / Addison Wesley Changing magnetic flux through a wire loop. f = 90o Alternator (AC generator) f = 90o DC generator Slidewire generator Magnetic force (F = IL x B) due to the induced current is toward the left, opposite to v. Lenz’s Law: The induced emf or current always tends to oppose or cancel the change that caused it. Lenz’s law Currents (I) induced in a wire loop. Motional induced emf (e): e=vBL because the potential difference between a and b is e = DV = energy / charge = W/q e = DV = work / charge DV = F x distance / q DV = (q v B) L / q so e=vBL Length and velocity are perpendicular to B Solenoid with increasing current I which induces an emf in the (yellow) wire. An induced current I’ is moved through the (yellow) wire by an induced electric field E in the wire. Eddy currents formed by induced emf in a rotating metal disk. Metal detector – an alternating magnetic field Bo induces eddy currents in a conducting object moved through the detector. The eddy currents in turn produce an alternating magnetic field B’ and this field induces a current in the detector’s receiver coil. A capacitor being charged by a current ic has a displacement current equal to iC between the plates, with displacement current iD = e A dE/dt. This changing E field can be regarded as the source of the magnetic field between the plates. A capacitor being charged by a current iC has a displacement current equal to iC between the plates, with displacement current iD = e A dE/dt From C = e A / d and DV = E d we can use q = C V to get q = (e A / d ) (E d ) = e E A = e F E and from iC = dq / dt = e A dE / dt = e dF E / dt = iD We have now seen that a changing E field can produce a B field, and from Faraday’s Law, a changing B field can produce an E field or emf. C 2009 J. Becker MAXWELL’S EQUATIONS The relationships between electric and magnetic fields and their sources can be stated compactly in four equations, called Maxwell’s equations. Together they form a complete basis for the relation of E and B fields to their sources. C 2004 Pearson Educational / Addison Wesley Determine direction of induced current for a) increasing B b) decreasing B Lenz’s law (Exercise 29.16) Lenz’s law (Exercise 29.17) Lenz’s law (Exercise 29.18) Motional emf and Lenz’s law (Exercise 29.22) Motional emf and Lenz’s law (Exercise 29.25) Review See www.physics.edu/becker/physics51 C 2009 J. Becker