Lesson Plans

Physics 1st Edition ©2002

by James S. Walker

Week 23

Chapter 23: Magnetic Flux and Faraday's Law of Induction

College Board Performance Objectives:

• Define magnetic flux giving its units.
• Explain how induced emf's are created by changing magnetic flux through a single loop.
• Predict the polarity of an induced emf.
• Describe ways in which magnetic flux can change.
• Discuss induced emf and current.
• Write Faraday's Law of Induction and apply it to induced emf through a loop.
• State Lenz's Law and use it to determine the direction of an induced current.
• Define inductance.
• Describe the main components of a DC motor and generator.
• Calculate the instantaneous and maximum emf and current generated by a simple generator.
• Explain how back emf reduces the net voltage delivered by a generator.
• Find the characteristic time interval in an RL circuit.
• Describe how to find the energy stored in an inductor.

College Board Lab Objectives:

• Determine the direction of the emf induced in a loop of wire moving through a magnetic field.
• To study the relationship between a magnetic field and the electric potential that can be induced by the field.

Suggested Labs:

• Induced Electrical Potential
• Simple Motors

Resources:

• Student Edition — pp. 748–776
• Student Study Guide — pp. 398–413
• Instructor's Solution Manual Volume 2 — pp. 73–82
• Instructor's Solution Manual CD — Chapter 23.doc
• Instructor's Resource Guide — pp. 94–97
• Test Items File — pp. 301–314
• Media Portfolio CD — Lecture Resources Chapter 23

Pacing Guide:

• Induced EMF—day 1
• Magnetic Flux—day 1
• Faraday's Law of Induction—days 1 and 2
• Lenz's Law—days 1 and 2
• Mechanical Work and Electrical Energy—days 2 and 3
• Motors and Generators—days 2 and 3
• Inductance—days 3 and 4
• RL Circuits—days 3 and 4
• Energy Stored in a Magnetic Field—day 4
• Transformers—day 4
• Lab—day 5
• Block Scheduling
  Induced EMF, Magnetic Flux, Faraday's Law of Induction, Lenz's Law, and Mechanical Work and Electrical Energy require a block-and-a-half. Motors and Generators, Inductance, RL Circuits, Energy Stored in a Magnetic Field, and Transformers also need a block-and-a-half.

Key Words:

Critical Thinking Questions:

1. A straight 6.0 cm wire is rotated around one of its ends through an angle of 90° in a time interval of 0.02 seconds. If, during this rotation, the wire is always perpendicular to a uniform field of flux density 0.25 Wb/m², what emf is induced between its ends?
2. A wire 8.0 m in length is located in the wing of an airplane in a region where the Earth's magnetic field has a value of 58.0 µT at 60° with the direction of the plane. If the induced emf is 41.0 mV, what is the speed of the airplane?
3. A solenoid 40.0 cm in length and diameter of 8.0 cm is wrapped with 500 turns of copper wire. When the solenoid carries a current of 10.0 A, what energy is stored in the inductor?
4. A square loop of wire 2.0 cm by 20.0 cm is located in a 600 gauss magnetic field directed out of the page. A bar with a resistance of 6.2 slides to the right along the loop at 2.5 m/s. (a) What is the induced emf in the loop? (b) What is the magnitude of the induced current?
5. An RL circuit consists of a 9.0 V battery, a 0.48 H inductor, and a 100.0 resistor connected in series with a switch. (a) What is the time constant for the circuit? (b) What is the current in the resistor 5.50 ms after the switch is closed? (c) What is the steady-state current? (d) What is the current in the resistor 2.5 ms after the switch is opened?
6. Solve problem 44 on p. 780 in the textbook.
7. Solve problem 70 on p. 781 in the textbook.

Answers: 1. 0.0354 V; 2. 370 km/h; 3. 0.197 ; 4. (a) 30 mV and (b) 4.8 mA; 5. (a) 4.8 ms, (b) 61.4 mA, (c) 90.0 mA, (d) 53.5 mA; 6. (a) 5.7 H, (b) 0.29 s, (c) 1.6 A; 7. (a) zero, (b) –vWB, (c) zero

Troubleshooting Tips/Error Traps:

• Faraday's Law is used to determine the magnitude of an induced emf.
• The negative sign in Faraday's Law is a reminder of Lenz's Law which is used to determine the direction of the induced emf.
• Students may think the existence of magnetic flux is sufficient to produce an induced emf. Stress that a change in magnetic flux is necessary to produce a motional emf.
• A steady magnetic field will not induce an emf. Only a changing magnetic flux will induce emf.
• Students may not properly identify the direction for motionally induced emf. Emphasizing Lenz's law and working through several examples will help.
• Show the students that a bar or rod pulled through a magnetic field in a perpendicular manner will behave as a seat of emf.

End of Chapter Activity:

1. Electric fields that circle back on themselves in closed loops are produced by
   1. point charges.
   2. electric dipoles.
   3. magnetic dipole moments.
   4. point charges moving at constant speed.
   5. a changing magnetic field.
2. A circular loop of copper wire of resistance R lies in the plane of the page. A magnetic field is directed through the loop out of the page. If the magnetic field is suddenly removed,
   1. a clockwise current is induced in the loop.
   2. an anticlockwise current is induced in the loop.
   3. no current is induced because the area remains constant.
   4. no current is induced because the loop does not rotate.
   5. no current is induced because a resistance is present.
3. The energy stored in a current carry inductor that is related to the self-inductance relates as
   1. inversely proportional to L.
   2. inversely proportional to L².
   3. directly proportional to L.
   4. directly proportional to L².
   5. directly proportional to .
4. Increasing the number of turns of wire in a coil placed in a region of changing magnetic field—while making no other changes—
   1. establishes an equilibrium.
   2. maintains a steady-state system.
   3. does not change the emf in the system.
   4. causes an increase in the induced emf.
   5. causes a decrease in the induced emf.
5. The emf across a coil of N turns subjected to a change in magnetic flux over a time interval equals
   1. 
   2. 
   3. 
   4. 
   5. 
6. A loop of N turns is rotated in a uniform magnetic field about an axis normal to the field. The direction of the induced current induced in the loop reverses every
   1. 0.25 revolution.
   2. 0.5 revolution.
   3. one revolution.
   4. 1.5 revolutions.
   5. two revolutions.
7. The inductance of a solenoid depends on
   1. the voltage across it.
   2. the current passing through it.
   3. its resistance.
   4. the magnetic field surrounding it.
   5. the geometry of the solenoid.
8. What is the time constant for a 0.0467 H inductor with a 33.0 resistance?
   1. 1.42 ms
   2. 2.84 ms
   3. 1.54 ms
   4. 70.7 ms
   5. 706.6 ms
9. When the south pole of a bar magnet approaches a loop, an emf is induced so that the magnetic field of the loop
   1. increases as the magnetic gets closer.
   2. decreases as the magnetic gets closer.
   3. points away from the south pole of the approaching magnet.
   4. points toward the south pole of the approaching magnet.
   5. none of the above statements is correct
10. Doubling the current in an inductor changes the energy stored in it by a factor of
    1. one-quarter.
    2. one-half.
    3. one.
    4. two.
    5. four.

Answers: 1 (e), 2 (b), 3 (c), 4 (d), 5 (a), 6 (b), 7 (e), 8 (a), 9 (c), 10 (e)

Suggested Conceptual Questions:

Suggested Problem Assignments: