chapter 29:electromagnetic induction and faraday’s law hw#9: chapter 28: pb.18, pb. 31, pb.40...

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Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

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Page 1: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

Chapter 29:Electromagnetic Induction and Faraday’s Law

HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

Page 2: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

29-2 Faraday’s Law of Induction; Lenz’s Law

Conceptual Example 29-1: Determining flux.

A square loop of wire encloses area A1. A uniform magnetic field B perpendicular to the loop extends over the area A2. What is the magnetic flux through the loop A1?

B!!!!!!!!!!!!!!

Page 3: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

Faraday’s law of induction: the emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit:

29-2 Faraday’s Law of Induction; Lenz’s Law

or

Page 4: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

29-2 Faraday’s Law of Induction; Lenz’s Law

Example 29-2: 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. What is the magnetic flux in the loop (a) when B is perpendicular to the face of the loop and (b) when B is at an angle of 30 to the area A of the loop? (c) What is the magnitude of the average current in the loop if it has a resistance of 0.012 Ω and it is rotated from position (b) to position (a) in 0.14 s?

B!!!!!!!!!!!!!!

B!!!!!!!!!!!!!!

A!!!!!!!!!!!!!!

Page 5: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

The minus sign gives the direction of the induced emf:

A current produced by an induced emf moves in a direction so that the magnetic field it produces

tends to restore the changed field.

or:

An induced emf is always in a direction that opposes the original change in flux that caused it.

THIS IS LENZ’S LAW

29-2 Faraday’s Law of Induction; Lenz’s Law

Page 6: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

Magnetic flux will change if the area of the loop changes.

29-2 Faraday’s Law of Induction; Lenz’s Law

Page 7: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

Magnetic flux will change if the angle between the loop and the field changes.

29-2 Faraday’s Law of Induction; Lenz’s Law

Page 8: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

Problem Solving: Lenz’s Law

1. Determine whether the magnetic flux is increasing, decreasing, or unchanged.

2. The magnetic field due to the induced current points in 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.

3. Use the right-hand rule to determine the direction of the current.

4. Remember that the external field and the field due to the induced current are different.

29-2 Faraday’s Law of Induction; Lenz’s Law

Page 9: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

29-2 Faraday’s Law of Induction; Lenz’s Law

Example 29-5: Pulling a coil from a magnetic field.A 100-loop square coil of wire, with side l = 5.00 cm and 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 abruptly 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) How much energy is dissipated in the coil? (d) What was the average force required (Fext)?

B!!!!!!!!!!!!!!

Page 10: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

This image shows another way the magnetic flux can change:

29-3 EMF Induced in a Moving Conductor

Page 11: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

The induced emf has magnitude

29-3 EMF Induced in a Moving Conductor

This equation is valid as long as B, , and v are mutually perpendicular (if not, it is true for their perpendicular components).

Page 12: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

The induced current is in a direction that tends to slow the moving bar – it will take an external force to keep it moving.

29-3 EMF Induced in a Moving Conductor

Page 13: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

3. Electric Force FE balances FB

29.3 Motional EMF

equilibrium

v

FB

-

-

FEL+ B

1. Moving rod in B-Field --> Electrons experience FB

2. electrons move in the direction of FB creating a charge separation and E-field

E

Page 14: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

Question

v

B

v

B

v

B

v

B

A conductor is moving downward in a magnetic field pointing into the page. Which sketch below shows the correct motional EMF and current directions?

EMFEMF EMF EMF

I I I I

A) B) C) D)

Page 15: Chapter 29:Electromagnetic Induction and Faraday’s Law HW#9: Chapter 28: Pb.18, Pb. 31, Pb.40 Chapter 29: Pb.3, Pb. 30, Pb. 48 Due Wednesday, April 22

29-3 EMF Induced in a Moving Conductor

Example 29-6: Does a moving airplane develop a large emf?

An airplane travels 1000 km/h in a region where the Earth’s magnetic field is about 5 x 10-5 T and is nearly vertical. What is the potential difference induced between the wing tips that are 70 m apart?