Chapter 31: Faraday’s Law

1. Chapter 31: Faraday’s Law

2. Chapter Outline • Induced EMF • Faraday’s Law of Induction • Lenz’s Law • EMF Inducedin a Moving Conductor • Electric Generators • Back EMF & Counter Torque • Eddy Currents • Transformers & Transmission of Power • A Changing Magnetic Flux • Produces an Electric Field • Applications of Induction: • Sound Systems, Computer Memory, Seismograph,….

3. Michael Faraday 1791 – 1867 • British physicist & chemist • Great experimental scientist Contributions to Electricity: 1. Electromagnetic induction 2. Laws of electrolysis Inventions 1. Motor 2. Generator 3. Transformer

4. Faraday Discovered: 1. Whenever the magnetic field about an electromagnet was made to grow & collapse by closing & opening the electric circuit of which it was a part, An electric current could be detected in a separate conductor nearby. 2. Moving a permanent magnet into & out of a coil of wire Also induced a current in the wire while the magnet was in motion. 3. Moving a conductor near a stationary permanent magnet caused a current to flow in the wire also, as long as it was moving.

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

6. He found no evidence when the current was steady. He saw • an induced current when the switch was turned on or off. • He concluded: • A Changing Magnetic Field Induces an EMF. • His experiment 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.

7. EMF Produced by a Changing Magnetic 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.

8. 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

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

10. Induced Current, Summary

11. 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.

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

13. 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.

14. Faraday’s Experiment: Conclusions • An electric current can be induced in a loop by a changing magnetic field. • This would be 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. • This is generally expressed as: An induced emf is produced in the loop by the changing magnetic field. • Just the existence of the magnetic flux is not sufficient to produce the induced emf, the flux must be changing.

15. 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 B is constant over the surface area A, then • 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.

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

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

18. 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?

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

20. 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.

21. 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.

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

23. 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

24. Example • A Loop of Wire in a Magnetic Field • A square loop of wire of side l = 5.0 cm is in a • uniform magnetic field B = 0.16 T. • Calculate • (a)The magnetic flux in the loop when B is • perpendicular to the face of the loop. • (b) The magnetic flux in the loop whenB is at an • angle of 30° to the area A of the loop, • (c) The magnitude of the average current in the loop • if it has a resistance of R = 0.012 Ω and it is • rotated from position (b) to position (a) in 0.14 s.

25. The Magnetic Flux will change if the area of the loop changes.

26. Magnetic Flux will change if the angle between the loop & the field changes.

27. Conceptual Example: Induction stove. In an induction stove, an ac current exists in a coil that is the “burner” (a burner that never gets hot). Why will it heat a metal pan but not a glass container?

28. Problem Solving: Lenz’s Law • Determine whether the magnetic flux is increasing, decreasing, or unchanged. • The magnetic field due to the induced currentpointsin the opposite direction to the original field if the flux is increasing; in the same direction if it is decreasing; and is zero if the flux is not changing. • Use the right-hand rule to determine the direction of the current. • Remember that the external field and the field due to the induced current are different.

29. Conceptual Example: Practice with Lenz’s Law In which direction is the current induced in the circular loop for each situation?

30. Example • Pulling a coil from a magnetic field. • A 100-loop square coil of wire, with • side l = 5.00 cm & total resistance • 100 Ω, is positioned perpendicular to • a uniform 0.600-T magnetic field. It • is quickly pulled from the field at • constant speed (moving perpendicular to • B) to a region where B drops to zero. • At t = 0, the right edge of the coil is at the edge of the field. It • takes 0.100 s for the whole coil to reach the field-free region. • Find: (a) the rate of change in flux through the coil, and • (b) the emf and current induced. • (c) the energy dissipated in the coil. • (d) the average force required (Fext).