# Last Homework. Reading: Chap. 33 and Chap. 33. Suggested exercises: 33.1, 33.3, 33.5, 33.7, 33.9, 33.11, 33.13, 33.15,

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1 Chapter 33. 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. Last Homework Reading: Chap. 33 and Chap. 33 Suggested exercises: 33.1, 33.3, 33.5, 33.7, 33.9, 33.11, 33.13, 33.15, Problems: 33.36, 33.37, 33.45, 33.49, 33.50, 33.52, 33.54, 33.55, 33.62, (Due Dec. 7) 1

2 Chapter 33. 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 Chapter 33. Basic Content and Examples 2

3 Electric Field versus Magnetic Field A current carrying wire generates magnetic field E Electric field magnetic field Question: Can a magnetic field generate the electric field or current? Faraday's Law Change of magnetic flux in a wire loop generates current! 3

4 Faraday's Law Change of magnetic flux in a wire loop generates emf: N: total number of loops Faraday's Law Fix area A Changing field B Fix field B Changing area A Magnitude & Direction 4

5 Changing Magnetic Field S N S N Change magnitude Change direction Changing Area Change magnitude Change direction 5

6 Lenz s Law The direction of the induced emf: The induced emf tends to generate a current that to create a magnetic flux to oppose the change of the magnetic flux through the area of the loop. Example 12.1 d L b x v B 6

7 Example 12.2 A rectangular loop of dimensions l and w, moved with a constant velocity v away from a long wire that carried a current I in the plane of the loop. The total resistance of the loop is R. Derive an expression that gives the current in the loop at the instant the near side is a distance r from the wire. Activity #1 7

8 Activity #2 Activity #3 8

9 Activity #4 Activity #5 9

10 Applications Generators Transformers V s = N s N p V p Metal detectors Applications Credit card readers 10

11 Induced Electric Field Changing B at the center of a loop of wire produces E in the wire. The electric field is still there even if the wire is removed. E E Faraday s Law Restated The changing magnetic field B induces an electric field E, and Thus, One of the Maxwell s equations 11

12 Induced Electric Field Symmetry shows that electric field lines make circular loops, whether or not there is a wire: E How do you determine the direction of E? Maxwell s Equations Gauss Law Faraday s Law Gauss Law Ampere s Law 12

13 Induced Electric & Magnetic Fields The generation of electromagnetic waves: Ampere s Law & Faraday s Law Inductor & Inductance Capacitor induces electric field Inductor generates magnetic field 13

14 Inductor & Inductance Unit: Henry (H) 1 H = 1 T m 2 /A Symbol: Inductance of a solenoid: L = μ 0N 2 A l N: number of turns A: cross-section area l: length Inductor & Inductance When a steady current passes through an inductor, if the inductor is ideal with R = 0, the potential difference across the inductor is zero. If the current is alternating as a function of time t, due to Faraday s law, the conductor will induce an emf which is against the change of the current. ε L = N dφ B dt According to the definition, NΦ B = Li Thus, ε L = L di dt 14

15 Inductor & Inductance According to Lenz s law, we have Or the potential drop from a to b point is ΔV = L di dt Energy Stored in an Inductor The power consumption: P = iδv The power consumed by an inductor is P = il di dt The stored magnetic energy U B by an inductor is When i = 0, U B = 0, then du B dt = il di dt U B = 1 2 Li2 U E = 1 2 CV2 Capacitor 15

16 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 16

17 EXAMPLE An AM radio oscillator QUESTION: EXAMPLE An AM radio oscillator 17

18 Chapter 33. Summary Slides General Principles 18

19 General Principles General Principles 19

20 Important Concepts Important Concepts 20

21 Applications Applications 21

22 Chapter 33. Clicker Questions A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor? 22

23 A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor? Is there an induced current in this circuit? If so, what is its direction? A. No B. Yes, clockwise C. Yes, counterclockwise 23

24 Is there an induced current in this circuit? If so, what is its direction? A. No B. Yes, clockwise C. Yes, counterclockwise 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. 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 24

25 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. 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 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. 25

26 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. 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. 26

27 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. 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. 27

28 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. 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 28

29 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 Chapter 33. Reading Quizzes 29

30 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 33. 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

31 Electromagnetic induction was discovered by A. Faraday. B. Henry. C. Maxwell. D. Both Faraday and Henry. E. All three. Electromagnetic induction was discovered by A. Faraday. B. Henry. C. Maxwell. D. Both Faraday and Henry. E. All three. 31

32 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. 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. 32

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