1. Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lecture prepared by Richard Wolfson Slide 27-1 27 Electromagnetic Induction Essential University Physics Richard Wolfson

2. Slide 27-2 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley In Chapter 27 you learnt To explain the phenomenon of electromagnetic induction To calculate induced emfs and currents To use energy conservation to find the direction of induced effects To describe important technological applications of induction To explain inductance And describe the role of inductance in simple circuits That magnetic fields store energy And how to calculate that energy To recognize Faraday’s law as one of the four fundamental laws of electromagnetism And to calculate induced electric fields

3. Slide 27-3 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Electromagnetic induction Electromagnetic induction involves electrical effects resulting from changing magnetic fields. Simple experiments (next slide) show that it doesn’t matter how the magnetic field changes: Induced electrical effects occur in all cases of changing magnetic fields. (1) Move a magnet near a circuit; an induced current results. (2) Move the circuit near a magnet; an induced current results. (3) Energize one coil to make it an electromagnet; move it near a circuit and an induced current results. (4) Energize one coil to make it an electromagnet; hold it stationary and move a circuit near it—an induced current results. (5) Change the current in one circuit, and thus the magnetic field it produces; an induced current results in a nearby circuit.

4. Slide 27-4 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Five simple experiments Experiment 1: moving magnet Experiment 2: moving circuit/coil Experiments 3 and 4: two circuits; either one moving Experiment 5: changing field/current; no motion

5. Slide 27-5 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Faraday’s law Faraday’s law, in its simplest form, describes induction by relating the emf induced in a circuit to the rate of change of magnetic flux through the circuit: Here the magnetic flux is given by With a flat area and uniform field, this becomes The flux can change because of changing field B, changing area A, or changing orientation  Moving a magnet near a wire loop increases the flux through the loop. The result is an induced emf given by Faraday’s law. The induced emf drives an induced current in the loop.

6. Slide 27-6 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Two examples: A changing field The loop has radius r, resistance R, and is in a magnetic field changing at the rate dB/dt. The induced emf is = πr 2 dB/dt and the induced current is I = (πr 2 /R) dB/dt. A changing area The bar slides on the conducting rails, increasing the circuit area at the rate l dx/dt = lv. The induced emf is = Blv, and the induced current is I = Blv/R.

7. Slide 27-7 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question What will be the direction of the current in the loop when it first enters the field shown, coming into the field from the left side? A.clockwise B.counterclockwise

8. Slide 27-8 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question What will be the direction of the current in the loop when it first enters the field shown, coming into the field from the left side? A.clockwise B.counterclockwise

9. Slide 27-9 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Direction of the induced current: Lenz’s law The direction of the induced emf and current is described by the minus sign in Faraday’s law. But it’s easier to get the direction from conservation of energy. The direction of the induced current must be such as to oppose that change that gives rise to it. This is known as Lenz’s law. Otherwise we could produce energy without doing any work! Here the north pole of the magnet approaches the loop. So the induced current makes the loop a bar magnet with north to the left, opposing the approaching magnet.

10. Slide 27-10 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley It’s the change that matters Lenz’s law says that induced effects oppose the changes that give rise to them. Now the induced current flows the opposite way, making the loop’s south pole to the left and opposing the withdrawal of the magnet.

11. Slide 27-11 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Electric generators Electric generators use a rotating coil in a magnetic field to convert mechanical to electrical energy. Here it’s the orientation  that’s changing to produce the changing magnetic flux. Lenz’s law makes it hard to turn a generator that’s supplying electrical energy. That’s why we have to burn fuels or use the energies of water or wind to generate electricity.

12. Slide 27-12 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A copper penny falls on a path that takes it between the poles of a magnet. Does the penny hit the ground going faster or slower than if the magnet were not present? A.The penny will hit the ground going faster. B.The penny will hit the ground going slower. C.The penny will hit the ground going the same speed either way.

13. Slide 27-13 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A copper penny falls on a path that takes it between the poles of a magnet. Does the penny hit the ground going faster or slower than if the magnet were not present? A.The penny will hit the ground going faster. B.The penny will hit the ground going slower. C.The penny will hit the ground going the same speed either way.

14. Slide 27-14 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Inductance Mutual inductance occurs when a changing current in one circuit results, via changing magnetic flux, in an induced emf and thus a current in an adjacent circuit. Mutual inductance occurs because some of the magnetic flux produced by one circuit passes through the other circuit. Self-inductance occurs when a changing current in a circuit results in an induced emf that opposes the change in the circuit itself. Self-inductance occurs because some of the magnetic flux produced in a circuit passes through that same circuit.

15. Slide 27-15 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A long wire carries a current I as shown. What is the direction of the current in the circular conducting loop when I is decreasing? A.The current flows counterclockwise. B.The current flows clockwise.

16. Slide 27-16 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question A long wire carries a current I as shown. What is the direction of the current in the circular conducting loop when I is decreasing? A.The current flows counterclockwise. B.The current flows clockwise.

17. Slide 27-17 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Self-inductance The self-inductance L of a circuit is defined as the ratio of the magnetic flux through the circuit to the current in the circuit: In differential form: Therefore, by Faraday’s law, the emf across an inductor is The minus sign shows that the direction of the inductor emf is such as to oppose the change in the inductor current.

18. Slide 27-18 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question Current flows from left to right through the inductor as shown. A voltmeter connected across the inductor gives a constant reading, and shows that the left end is positive. Is the current in the inductor changing, and if so, how? A.The current is increasing. B.The current is decreasing. C.The current is constant.

19. Slide 27-19 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Clicker question Current flows from left to right through the inductor as shown. A voltmeter connected across the inductor gives a constant reading, and shows that the left end is positive. Is the current in the inductor changing, and if so, how? A.The current is increasing. B.The current is decreasing. C.The current is constant.

20. Slide 27-20 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Magnetic energy As current builds up in an inductor, the inductor absorbs energy from the circuit. That energy is stored in the inductor’s magnetic field. For an inductor, the stored energy is Considering the uniform magnetic field inside a solenoid shows that the magnetic energy density is This is a universal expression: wherever there’s a magnetic field, there’s energy with density B 2 /2  0.

21. Slide 27-21 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Induced electric fields The induced emf in a circuit subject to changing magnetic flux results from an induced electric field. Induced electric fields result from changing magnetic flux. This is described by the full form of Faraday’s law, one of the four fundamental laws of electromagnetism: where the integral is taken around any closed loop, and where the flux is through any area bounded by the loop. Loosely, Faraday’s law states that a changing magnetic field produces an electric field. Thus not only charges but also changing magnetic fields are sources of electric field. Unlike the electric field of a static charge distribution, the induced electric field is not conservative. O

22. Slide 27-22 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Static and induced electric fields Static electric fields begin and end on charges. But induced electric fields generally form closed loops.

23. Slide 27-23 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Summary Faraday’s law describes electromagnetic induction, most fundamentally the phenomenon whereby a changing magnetic field produces an electric field: This induced electric field is nonconservative and its field lines have no beginnings or endings. In the presence of a circuit, the induced electric field gives rise to an induced emf and an induced current. Lenz’s law states that the direction of the induced current is such that the magnetic field it produces acts to oppose the change that gives rise to it. Self-inductance is a circuit property whereby changing current in a circuit results in an induced emf that opposes the change. Consideration of current buildup in an inductor shows that all magnetic fields store energy, with energy density B 2 /2  0. O

24. Slide 27-24 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Magnetic induction and Faraday’s law Ch 27 Problem 40 A square wire loop with sides of 3.0 m is perpendicular to a uniform magnetic field of 2.0 T. A 6.0 V light bulb is in series with the loop. The magnetic field is reduced steadily to zero over time ∆t. (a)Find ∆t such that the light will shine at full brightness during this time. (b)Which way will the loop current flow?

25. Slide 27-25 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley (a) State Faraday’s law and Lenz’s law using words as well as symbols. Explain all symbols that you use. [6] (b) A small circular copper ring is inside a larger loop that is connected to a battery and a switch as shown in the figure. Use Lenz’s law to find the direction of the current induced in the small ring (i)just after switch S is closed, (ii)after S has been closed a long time and (iii) just after S has been reopened after being closed a long time. [4]

26. Slide 27-26 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley Magnetic induction and Faraday’s law Ch 27 Exercise 18 A conducting loop of area 240 cm 2 and resistance 12 Ω lies at right angles to a spatially uniform magnetic field. The loop carries an induced current of 320 mA. At what rate is the magnetic field changing? Ch 27 Exercise 19 The magnetic field inside a 20 cm diameter solenoid is increasing at a rate of 2.4 T/s. How many turns should a coil wrapped around the outside of the solenoid have so that the emf induced in the coil is 15 V? Both on Sheet 10