Ch. 21: Magnetic Induction & Faraday’s Law of Induction

1. Ch. 21: Magnetic Induction & Faraday’s Law of Induction

2. Topics Outline • Induced EMF • Faraday’s Law • of Induction • Lenz’s Law • EMF Inducedin a Moving • Conductor • Electric Generators • Back EMF & Counter Torque

3. More Topics • Eddy Currents • Transformers& Transmission of Power • Faraday’s Law: • A Changing Magnetic Flux • Produces an Electric Field! • Some Applications of Induction: • Sound Systems, Computer Memory, Seismograph,….

4. Magnetic Induction • Electric & magnetic forces both act only on particles carrying an electric charge • Ch. 20: Moving electric charges create a magnetic field • Ch. 21 (now!): A changing magnetic field creates an electric field • This effect is called magnetic induction • This links electricity and magnetism in a fundamental way • Magnetic induction is also the key to many practical applications. See next slides!

5. Some Applications Magnetic Resonance Imaging (MRI) Speedometers & Odometers

6. Electric Guitars & Other Instruments

7. Hybrid Automobiles

8. Electromagnetism • Electric and magnetic phenomena were first connected by Ørsted in 1820 • He discovered that an electric current in a wire can exert a force on a compass needle. • We just saw this in the last chapter. • This indicates that an electric field can lead to a force on a magnet. • We just saw this in the last chapter • He concluded that An electric field can produce a magnetic field

9. An electric field can produce a magnetic field

10. An electric field can produce a magnetic field • Eventually, this led to the question: Can a magnetic field produce an electric field?

11. An electric field can produce a magnetic field • Eventually, this led to the question: Can a magnetic field produce an electric field? • Experiments by Michael Faraday found that the answer is yes!

12. Michael Faraday 1791 – 1867 • British physicist & Chemist. • Great experimental Scientist. • A “hands” on Experimental Scientist. Strong on experiment design. Less strong on math! 2 of his Major Contributions to Electricity: 1. Electromagnetic induction 2. Laws of electrolysis (Chemistry)

13. Michael FaradayA Productive Inventor!!! Some Major Inventions 1. Motor 2. Generator 3. Transformer

14. Faraday’s Discoveries: 1. Whenever the magnetic field about an electromagnet was made to grow or collapse by closing or opening the electric circuit of which it was a part, an electric current could be detected in a separate conductor nearby.

15. Faraday’s Discoveries: 2. Moving a permanent magnet into & out of a coil of wire also induces a current in the wire while the magnet is moving. 3. Moving a conductor near a stationary permanent magnet causes a current to flow in the wire also, as long as it is moving.

16. Faraday’s Experiments • Faraday attempted to observe a B field-induced E field • He used an ammeter instead of a light bulb • If the bar magnet was in motion, a current was observed • If the magnet was stationary, the current & the electric field were both zero

17. Another Faraday Experiment • A solenoid is positioned near a loop of wire with the light bulb. Current passes through the solenoid by connecting it to a battery. When the current through the solenoid is constant, there is no current in the wire. When the switch is opened or closed, the bulb lights up.

18. Induced EMF • Faraday looked for evidence that a • magnetic field would induce an electric • current with this apparatus:

19. He found no evidence when the current was • steady. But, he saw an induced current • when the switch was turned on or off.

20. Faraday concluded that: A Changing Magnetic Field Induces an EMF. • His experiments used a magnetic field that • was changing because the current producing it • was changing; the picture shows a magnetic • field that changes because the magnet is moving.

21. An EMF is Produced by a ChangingMagnetic Field • A loop of wire is connected to a sensitive ammeter. • When a magnet is moved toward the loop, the ammeter deflects. • The direction was arbitrarily chosen to be negative.

22. When the magnet is held stationary, there is no deflection of the ammeter. • Therefore, there is no induced current. • Even though the magnet is in the loop

23. If the magnet is moved away from the loop. • The ammeter deflects in the opposite direction!

24. Induced Current, Summary

25. Faraday’s Experiment – Set Up • A primary coil is connected to a switch and a battery. • The wire is wrapped around an iron ring. • A secondary coil is also wrapped around the iron ring. No battery is present in the secondary coil. • The secondary coil is not directly connected to the primary coil.

26. Close the switch &observe the current readings on the ammeter.

27. Faraday’s Findings • At the instant the switch is closed, the ammeter changes from zero in one direction, then returns to zero. • When the switch is opened, the ammeter changes in the opposite direction, then returns to zero. • The ammeter reads zero when there is a steady current or when there is no current in the primary circuit.

28. Faraday’s Experiments: Conclusions • An electric currentcan be induced in a loop by a changing magnetic field. • This is the current in the secondary circuit of this experimental set-up. • The induced current exists only while the magnetic field through the loop is changing.

29. Faraday’s Experiments: Conclusions • An electric current is induced in a secondary circuit during the time when the current through the solenoid is changing. Faraday’s experiments show that an electric current is produced in the wire loop only when the magnetic field at the loop is changing A changing magnetic field produces an electric field

30. Faraday’s Experiments: Conclusions A changing magnetic field produces an electric field • An electric field produced in this way is called an induced electric field. • This phenomena is called electromagnetic induction

31. Faraday’s Experiment: Conclusions • All of this is usually expressed as: An induced emf is produced in the loop by the changing magnetic field. • Just the existence of the magnetic field is not sufficient to produce the induced emf, the field must be changing.

32. Magnetic Flux • Faraday developed a quantitative theory of induction that is now called Faraday’s Law • This law shows how to calculate the induced electric field in different situations • Faraday’s Law uses the concept of magnetic flux • Magnetic flux is similar to the concept of electric flux • Let A be an area of a surface with a magnetic field passing through it • The flux is defined as ΦB B A cosθ

33. Magnetic Flux • If the field is perpendicular to the surface, ΦB = B A • If the field makes an angle θ with the normal to the surface, ΦB = B A cosθ • If the field is parallel to the surface, ΦB = 0

34. The magnetic flux can be defined for any surface • A complicated surface can be broken into small regions and the definition of flux applied • The total flux is the sum of the fluxes through all the individual pieces of the surface • The surfaces of interest are open surfaces • With electric flux, closed surfaces were used • SI unit of magnetic flux = the Weber (Wb) 1 Wb = 1 T . m2

35. Faraday’s Law of Induction: Lenz’s Law • Faraday found that the induced emfin a wire loop is • Proportional to the time Rate of Change of the Magnetic Flux Through the Loop. • Magnetic Flux is definedsimilarly to electric • flux: If Bis constant over a surface areaA, • then the magnetic flux passing through A is • ΦB BA = BA cosθ • (The scalar or dot product of vectors B & A) • The SI Unit of Magnetic flux = Weber (Wb): • 1 Wb = 1 T·m2.

36. This figure shows the variables in the flux equation: ΦB = BA = BA cosθ

37. Magnetic Fluxis analogous to electric flux: It • is proportional to the total number of • magnetic field linespassing through the loop.

38. Conceptual Example: Determining Flux • A square loop of wire encloses areaA1.A uniform • magnetic fieldBperpendicular to the loop extends • over the areaA2. • What is the magnetic flux through the loopA1?

39. Faraday’s Law of Induction: “The emf inducedin a circuit is equal to the negative of the time rate of change of magnetic flux through the circuit.” For a coil of N turns: N

40. Faraday’s Law, Summary Only changes in the magnetic flux matter • Rapid changes in the flux produce larger values of emf than do slow changes • This dependence on frequency means the induced emf plays an important role in AC circuits • The magnitude of the emf is proportional to the rate of change of the flux

41. Faraday’s Law, Summary • The magnitude of the induced emf is proportional to the rate of change of the flux • If the rate is constant, then the emf is constant • In most cases, this isn’t possible and AC currents result • The induced emf is present even if there is no current in the path enclosing an area of changing magnetic flux

42. Flux Though a Changing Area • A magnetic field is constant and in a direction perpendicular to the plane of the rails and the bar. • Assume the bar moves at a constant speed. • The magnitude of the induced emf is ε = B L v • The current leads to power dissipation in the circuit

43. Conservation of Energy • The mechanical power put into the bar by the external agent is equal to the electrical power delivered to the resistor • Energy is converted from mechanical to electrical, but the total energy remains the same • Conservation of energy is obeyed by electromagnetic phenomena

44. The minus sign gives the directionof • the induced emf. •  Lenz’s Law: • A current produced by an induced emf moves in a direction so that the magnetic field • it produces • tends to restore the changed field.

45. The minus sign gives the directionof • the induced emf. •  Lenz’s Law: • Alternative Statement: • An induced emf is always • in a direction that OPPOSES • the original change in flux • that caused it.

46. Lenz’s Law • Lenz’s Lawgives a way to determine the sign of the induced emf • Lenz’s Lawstates that the magnetic field produced by an induced current always opposes any changes in the magnetic flux

47. Lenz’s Law, Example 1 • Assume a metal loop in which the magnetic field passes upward through it. Assume the magnetic flux increases with time. • The magnetic field produced by the induced emf must oppose the change in flux. So, the induced magnetic field must be downward and the induced current will be clockwise

48. Lenz’s Law, Example 2 • Assume a metal loop in which the magnetic field passes upward through it. Assume the magnetic flux decreases with time. • The magnetic field produced by the induced emf must oppose the change in flux. So, the induced magnetic field must be upward and the induced current will be counterclockwise

49. Example • Assume a loop enclosing an area A that lies in a uniform magnetic field. • The magnetic flux through the loop is ΦB = BA = BAcos(θ) • The induced emf is •  = - ([BAcos(θ)]/t)

50. The magnitude of the magnetic field can change with time. The area enclosed by the loop can change with time. The angle between the magnetic field & the normal to the loop can change with time. Any combination of the above can occur. Methods of Inducing an EMF Using Faraday’s Law