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Electromagnetic Induction Ch. 29 Induction experiments Faraday’s law Lenz’s law Motional electromotive force Induced electric fields Eddy currents Displacement Current C 2012 J. F. Becker (sec. 29.1) (sec. 29.2) (sec. 29.3) (sec. 29.4) (sec. 29.5) (sec. 29.6) (sec. 29.7) Learning Goals - we will learn: ch 29 • The experimental evidence that a changing magnetic field induces an emf ! • How Faraday’s Law relates the induced emf in a loop to the change in magnetic flux through the loop. • How a changing magnetic flux generates an electric field that is very different from that produced by an arrangement of charges. • Four fundamental equations completely describe both electricity and magnetism. Current induced in a coil. When B is constant and the shape, location, and orientation of the coil does not change, the induced current is zero in the coil. 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. O O Lenz’s law Faraday’s Law of Induction How electric generators, credit card readers, and transformers work. Eqn 29.3 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 velocity v. Lenz’s Law The induced emf (or current) always tends to oppose or cancel the change that caused it. O O 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. DISPLACEMENT CURRENT A capacitor being charged by a current iC has a “displacement current” between the plates equal to iC , 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. ( E _ B ) 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 now see 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 2011 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 29.21) Motional emf and Lenz’s law (Exercise 29.26) TRANSFORMERS can step-up AC voltages or step-down AC voltages. Lenz’s law (Exercise 29.18) e = -N dF B / dt TRANSFORMERS can step-up AC voltages or stepdown AC voltages. e2 /e1 = N /N 2 V1I1 = V2I1 1 FB = FB Transformer: AC source is V1 and secondary provides a voltage V2 to a device with resistance R. Figure 32.2b Large step-down transformers at power stations are immersed in tanks of oil for insulation and cooling. Figure 31.22 Figure 31.23 Review See www.physics.sjsu.edu/becker/physics51 C 2012 J. F. Becker