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Induction experiments(sec. 29.1) Faraday’s law (sec. 29.2) Lenz’s law(sec. 29.3) Motional electromotive force(sec. 29.4) Induced electric fields(sec. 29.5) Eddy currents(sec. 29.6) Displacement Current(sec. 29.7) Electromagnetic Induction Ch. 29 C 2012 J. F. Becker

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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.

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Current induced in a coil.

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When B is constant and the shape, location, and orientation of the coil does not change, the induced current is zero in the coil.

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Conducting loop in increasing B field.

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Magnetic flux through an area.

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Lenz’s law Lenz’s Law The induced emf (or current) always tends to oppose or cancel the change that caused it. O O

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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 Eqn 29.3

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Changing magnetic flux through a wire loop.

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Alternator (AC generator) = 90 o

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DC generator = 90 o

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Slidewire generator

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Magnetic force (F = IL x B) due to the induced current is toward the left, opposite to velocity v.

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Lenz’s law Lenz’s Law The induced emf (or current) always tends to oppose or cancel the change that caused it. O O

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Currents (I) induced in a wire loop.

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Motional induced emf ( e ): e = v B L because the potential difference between a and b is e = D V = energy / charge = W/q e = D V = work / charge D V = F x distance / q D V = (q v B) L / q so e = v B L Length and velocity are perpendicular to B

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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.

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Eddy currents formed by induced emf in a rotating metal disk.

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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.

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A capacitor being charged by a current i C has a “displacement current” between the plates equal to i C, with displacement current i D = e A dE/dt. This changing E field can be regarded as the source of the magnetic field between the plates. ( E _ B ) DISPLACEMENT CURRENT

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A capacitor being charged by a current i C has a displacement current equal to i C between the plates, with displacement current i D = e A dE/dt From C = e A / d and D V = E d we can use q = C V to get q = ( e A / d ) (E d ) = e E A = e F E and from i C = dq / dt = e A dE / dt = e d F E / dt = i D 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

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MAXWELL’S EQUATIONS C 2004 Pearson Educational / Addison Wesley 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.

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Determine direction of induced current for a) increasing B b) decreasing B Lenz’s law (Exercise 29.16)

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Lenz’s law (Exercise 29.17)

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Lenz’s law (Exercise 29.18)

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Motional emf and Lenz’s law (Exercise 29.21)

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Motional emf and Lenz’s law (Exercise 29.26)

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TRANSFORMERS can step-up AC voltages or step-down AC voltages.

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Lenz’s law (Exercise 29.18)

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Transformer: AC source is V 1 and secondary provides a voltage V 2 to a device with resistance R. TRANSFORMERS can step-up AC voltages or step- down AC voltages. 2 / 1 = N 2 /N 1 V 1 I 1 = V 2 I 1 = e = -N d F B / dt

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Figure 32.2b

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Large step-down transformers at power stations are immersed in tanks of oil for insulation and cooling.

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Figure 31.22

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Figure 31.23

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See www.physics.sjsu.edu/becker/physics51 Review C 2012 J. F. Becker

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