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. Chapter 34. Electromagnetic Induction Topics: Induced Currents Motional emf Magnetic Flux Lenz’s Law Faraday’s Law Induced Fields Induced Currents: Three Applications Inductors LC Circuits LR Circuits

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 34. Reading Quizzes

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Currents circulate in a piece of metal that is pulled through a magnetic field. What are these currents called? A.Induced currents B.Displacement currents C.Faraday’s currents D.Eddy currents E.This topic is not covered in Chapter 34.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Currents circulate in a piece of metal that is pulled through a magnetic field. What are these currents called? A.Induced currents B.Displacement currents C.Faraday’s currents D.Eddy currents E.This topic is not covered in Chapter 34.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electromagnetic induction was discovered by A.Faraday. B.Henry. C.Maxwell. D.Both Faraday and Henry. E.All three.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electromagnetic induction was discovered by A.Faraday. B.Henry. C.Maxwell. D.Both Faraday and Henry. E.All three.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The direction that an induced current flows in a circuit is given by A.Faraday’s law. B.Lenz’s law. C.Henry’s law. D.Hertz’s law. E.Maxwell’s law.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The direction that an induced current flows in a circuit is given by A.Faraday’s law. B.Lenz’s law. C.Henry’s law. D.Hertz’s law. E.Maxwell’s law.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 34. Basic Content and Examples

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Faraday’s Discovery Faraday found that there is a current in a coil of wire if and only if the magnetic field passing through the coil is changing. This is an informal statement of Faraday’s law.

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 creates an induced current in the coil. This current is amplified into a sequence of voltage pulses that represent the 0s and 1s of digital data.

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Motional emf The motional emf of a conductor of length l moving with velocity v perpendicular to a magnetic field B is

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.1 Measuring the earth’s magnetic field QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.1 Measuring the earth’s magnetic field

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.1 Measuring the earth’s magnetic field

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.1 Measuring the earth’s magnetic field

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Magnetic flux can be defined in terms of an area vector

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Magnetic Flux The magnetic flux measures the amount of magnetic field passing through a loop of area A if the loop is tilted at an angle θ from the field, B. As a dot-product, the equation becomes:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.4 A circular loop in a magnetic field QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 34.4 A circular loop in a magnetic field

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Lenz’s Law There is an induced current in a closed, conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in the flux.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Tactics: Using Lenz’s Law

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Faraday’s Law An emf is induced in a conducting loop if the magnetic flux through the loop changes. The magnitude of the emf is and the direction of the emf is such as to drive an induced current in the direction given by Lenz’s law.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: Electromagnetic Induction

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Inductance of a solenoid The inductance of a solenoid having N turns, length l and cross-section area A is

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE The length of an inductor QUESTION:

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The potential difference across an inductor The potential difference across an inductor with an inductance of L and carrying a current I is

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE Large voltage across an inductor QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE Large voltage across an inductor

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE Large voltage across an inductor

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE Large voltage across an inductor

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The current in an LC circuit The current in an LC circuit where the initial charge on the capacitor is Q 0 is The oscillation frequency is given by

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE An AM radio oscillator QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE An AM radio oscillator

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 34. Summary Slides

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 34. Clicker Questions

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Is there an induced current in this circuit? If so, what is its direction? A.No B.Yes, clockwise C.Yes, counterclockwise

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.No B.Yes, clockwise C.Yes, counterclockwise Is there an induced current in this circuit? If so, what is its direction?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. F b = F d > F a = F c B. F c > F b = F d > F a C. F c > F d > F b > F a D. F d > F b > F a = F c E. F d > F c > F b > F a A square loop of copper wire is pulled through a region of magnetic field. Rank in order, from strongest to weakest, the pulling forces F a, F b, F c and F d that must be applied to keep the loop moving at constant speed.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. F b = F d > F a = F c B. F c > F b = F d > F a C. F c > F d > F b > F a D. F d > F b > F a = F c E. F d > F c > F b > F a A square loop of copper wire is pulled through a region of magnetic field. Rank in order, from strongest to weakest, the pulling forces F a, F b, F c and F d that must be applied to keep the loop moving at constant speed.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current? A.There is no current around the loop. B.There is a clockwise current around the loop. C.There is a counterclockwise current around the loop.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.There is no current around the loop. B.There is a clockwise current around the loop. C.There is a counterclockwise current around the loop. A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. What happens to the loop? A.The loop is pulled to the left, into the magnetic field. B.The loop is pushed to the right, out of the magnetic field. C.The loop is pushed upward, toward the top of the page. D.The loop is pushed downward, toward the bottom of the page. E.The tension is the wires increases but the loop does not move.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.The loop is pulled to the left, into the magnetic field. B.The loop is pushed to the right, out of the magnetic field. C.The loop is pushed upward, toward the top of the page. D.The loop is pushed downward, toward the bottom of the page. E.The tension is the wires increases but the loop does not move. A conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. What happens to the loop?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The potential at a is higher than the potential at b. Which of the following statements about the inductor current I could be true? A.I is from b to a and is steady. B.I is from b to a and is increasing. C. I is from a to b and is steady. D. I is from a to b and is increasing. E. I is from a to b and is decreasing.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.I is from b to a and is steady. B.I is from b to a and is increasing. C. I is from a to b and is steady. D. I is from a to b and is increasing. E. I is from a to b and is decreasing. The potential at a is higher than the potential at b. Which of the following statements about the inductor current I could be true?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Rank in order, from largest to smallest, the time constants τ a, τ b, and τ c of these three circuits. A. τ a > τ b > τ c B. τ b > τ a > τ c C. τ b > τ c > τ a D. τ c > τ a > τ b E. τ c > τ b > τ a

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. τ a > τ b > τ c B. τ b > τ a > τ c C. τ b > τ c > τ a D. τ c > τ a > τ b E. τ c > τ b > τ a Rank in order, from largest to smallest, the time constants τ a, τ b, and τ c of these three circuits.