# Electromagnetic Induction

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## Video Clips

RealVideo®
6:34 minutes (23:46 - 30:20)

Examples of Faraday's Law with a fixed loop in a changing magnetic field, and for a loop with changing area in a constant magnetic field.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Motional EMF in Space

RealVideo®
3:56 minutes (30:20 - 34:16)

Discussion of a 1996 experiment in which NASA attached a 20 kilometer conducting wire to the space shuttle and measured the induced current as it flew through space.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Transformers

RealVideo®
10:35 minutes (21:28 - 32:03)

Definition, including primary and secondary coils and equations for the voltage and current relative to the number of windings in each coil. How transformers are used to step the voltage up and down in power lines that transfer electricity.

Prior Knowledge: Self Inductance (Beginning of video lecture 20)
Instructor: Prof. Walter Lewin

#### Demonstration: Transformers

RealVideo®
9:46 minutes (32:03 - 41:49)

Showing the voltages in a transformer with a 220 winding primary coil and a 1 to 4 winding secondary coil. Showing that huge currents can be produced using transformers by melting a nail with a single winding secondary coil.

Prior Knowledge: Transformers (21:28 of video lecture 24)
Instructor: Prof. Walter Lewin

#### Spark Plugs

RealVideo®
8:33 minutes (41:49 - 50:22)

How transformers are used to create huge voltages and sparks from a 12V car battery. Includes a demonstration.

Prior Knowledge: Transformers (21:28 of video lecture 24)
Instructor: Prof. Walter Lewin

#### Review: Transformers

RealVideo®
3:23 minutes (3:05 - 6:28)

Step-up and step-down transformers, with equations relating that ratio of voltage and current to the ratio of the number of turns in the two coils.

Prior Knowledge: Transformers (21:28 of video lecture 24)
Instructor: Prof. Walter Lewin

#### Diamagnetism

RealVideo®
4:07 minutes (6:03 - 10:10)

Definition, including the properties of diamagnetic materials.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Paramagnetism

RealVideo®
4:46 minutes (10:10 - 14:56)

The properties of paramagnetic materials, including a comparison to diamagnetism.

Prior Knowledge: Diamagnetism (6:03 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Ferromagnetism

RealVideo®
5:02 minutes (14:56 - 19:58)

Definition, including discussion of domains in ferromagnetic materials. Comparison between paramagnetic and ferromagnetic materials.

Prior Knowledge: Paramagnetism (10:10 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Demonstration: Ferromagnetism

RealVideo®
5:50 minutes (19:58 - 25:48)

Showing the strength of the attraction between ferromagnetic materials and magnetic fields using a 15kg metal bar which is sucked into the magnetic field of a solenoid. Illustrating the concept of ferromagnetic domains using an array of compass needles.

Prior Knowledge: Ferromagnetism (14:56 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Demonstration: Ferromagnetic Domains

RealVideo®
4:48 minutes (25:48 - 30:36)

Hearing the domains in a ferromagnetic material flip by connecting an amplifier to a solenoid wrapped around the ferromagnetic material and then approaching it with a magnet.

Prior Knowledge: Ferromagnetism (14:56 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Relative Permeability

RealVideo®
5:12 minutes (30:36 - 35:48)

Definition, including characterization for diamagnetic, paramagnetic, and ferromagnetic materials. The Curie point for ferromagnetic materials is also defined.

Prior Knowledge: Diamagnetism, Paramagnetism, and Ferromagnetism (6:03 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Demonstration: Curie Point for Iron

RealVideo®
4:27 minutes (35:48 - 40:15)

Showing that an iron washer is no longer attracted to a magnet when heated above the Curie point for iron.

Prior Knowledge: Relative Permeability (30:36 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Demonstration: Liquid Oxygen

RealVideo®
6:06 minutes (40:15 - 46:21)

Showing that liquid oxygen, although paramagnetic, will be attracted to a strong magnet.

Prior Knowledge: Paramagnetism (10:10 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Review: Diamagnetism, Paramagnetism, and Ferromagnetism

RealVideo®
3:05 minutes (0:00 - 3:05)

The properties of each, including the Curie temperature and the magnetic field in a solenoid with ferromagnetic material inside.

Prior Knowledge: Diamagnetism, Paramagnetism, and Ferromagnetism (6:03 of video lecture 21)
Instructor: Prof. Walter Lewin

#### Electromagnetic Induction and Lenz's Law

RealVideo®
5:32 minutes (4:58 - 10:30)

Introduction to the concept that a changing magnetic field can induce a current.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Demonstration: Electromagnetic Induction

RealVideo®
2:00 minutes (10:30 - 12:30)

Showing that a current is induced in a coil of wire when a bar magnet is moved near or away from it.

Prior Knowledge: Electromagnetic Induction (4:58 of video lecture 16)
Instructor: Prof. Walter Lewin

RealVideo®
10:14 minutes (12:30 - 22:44)

Derivation of Faraday's Law, with a statement of the four almost complete Maxwell's Equations.

Prior Knowledge: Electromagnetic Induction (4:58 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Using Faraday's Law

RealVideo®
4:33 minutes (22:44 - 27:17)

Conventions for choosing the direction of dA, explanation of why any open surface can be used, and listing of steps for using Faraday's Law.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Demonstration: Faraday's Law

RealVideo®
6:25 minutes (27:17 - 33:42)

Showing that a current will be induced in a loop of wire wrapped around a solenoid when a current is run through that solenoid. Also shows that the induced current increases when there are more loops wrapped around the solenoid.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Non-Conservative Fields

RealVideo®
10:50 minutes (33:42 - 44:32)

If there is changing magnetic flux through a circuit, Kirchhoff's rules no longer apply because the electric field through the circuit is no longer conservative. In this nonconservative field, the potential difference depends upon the path.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Demonstration: Non-Conservative Fields

RealVideo®
6:54 minutes (44:32 - 51:26)

Showing that different voltages can be measured across the same points in a circuit when there is an induced current through the circuit.

Prior Knowledge: Non-Conservative Fields (33:42 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Faraday's Law: Changing the Magnetic Flux

RealVideo®
5:00 minutes (0:00 - 5:00)

Quick review of Faraday's Law for a conducting loop in a magnetic field. Can change the flux through the loop by changing the area of the loop, the strength of the magnetic field, or the angle between the loop and the field.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Conducting Loop Rotating in a Uniform Field

RealVideo®
5:32 minutes (5:00 - 10:32)

Worked example of Faraday's Law with a changing angle between the loop and the magnetic field.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Demonstration: Conducting Loop Rotating in a Uniform Field

RealVideo®
7:45 minutes (10:32 - 18:17)

Showing that a current is induced in a coil of wire when it is rotated in the magnetic field of the earth.

Prior Knowledge: Conducting Loop Rotating in a Uniform Field (5:00 of video lecture 17)
Instructor: Prof. Walter Lewin

#### Electric Generators

RealVideo®
6:30 minutes (18:17 - 24:47)

Brief discussion of how electric generators work, as well as differences in voltage and frequency of electricity delivered in the US and in Europe.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Demonstration: Electric Generators

RealVideo®
4:07 minutes (24:47 - 28:54)

Student tries to light up light bulbs with a hand powered generator. Also an example of a flashlight and a radio which each have a built in generator.

Prior Knowledge: Electric Generators (18:17 of video lecture 17)
Instructor: Prof. Walter Lewin

#### Conducting Loop with a Moving Crossbar in a Uniform Field

RealVideo®
7:04 minutes (28:54 - 35:58)

Worked example of Faraday's Law with a conducting loop that has changing area.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Eddy Current Braking

RealVideo®
5:56 minutes (35:58 - 41:54)

Definition of magnetic braking, with a demonstration of a copper pendulum swinging through a magnetic field.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Demonstration: Conducting Coil Moving Into a Magnetic Field

RealVideo®
2:48 minutes (41:54 - 44:42)

Showing that a bulb connected to a coil of copper wire lights up when the coil is moved into or out of a magnetic field.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Demonstrating: Magnetic Braking

RealVideo®
6:09 minutes (44:42 - 50:51)

Showing that a conducting ring slows down as it is falling into or out of a magnetic field.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Three Phase Currents: Synchronous and Induction Motors

RealVideo®
10:25 minutes (23:27 - 33:52)

Definitions, with examples of tools that use induction motors including the table saw and lawnmower.

Prior Knowledge: Faraday's Law (12:30 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Demonstration: Three Phase Motor

RealVideo®
3:21 minutes (33:52 - 37:13)

Showing the behavior of bar magnets, a conducting egg, and a conducting ring when placed in the magnetic field of a three phase generator.

Prior Knowledge: Three Phase Currents (23:27 of video lecture 18)
Instructor: Prof. Walter Lewin

#### Secret Top Explained

RealVideo®
9:50 minutes (37:13 - 47:03)

Discussion of the secret top and how it works, with a repeat of the demo from a previous lecture.

Prior Knowledge: Secret Top (video lecture 12)
Instructor: Prof. Walter Lewin

#### Two Phase Current

RealVideo®
4:09 minutes (47:03 - 51:12)

Definition, with a demonstration of a coffee can rotating in the magnetic field of a two phase generator.

Prior Knowledge: Three Phase Currents (23:27 of video lecture 18)
Instructor: Prof. Walter Lewin

#### Superconductivity

RealVideo®
7:53 minutes (27:13 - 35:06)

Definition, with explanation of the original discovery of superconductors.

Prior Knowledge: none
Instructor: Prof. Walter Lewin

#### Magnetic Levitation with Superconductors

RealVideo®
2:59 minutes (35:06 - 38:05)

Using a superconductor to levitate a magnet, including a demo.

Prior Knowledge: Superconductivity (27:13 of video lecture 19)
Instructor: Prof. Walter Lewin

#### Maglev Trains

RealVideo®
3:59 minutes (38:05 - 42:04)

How magnets are being used to create very fast, almost frictionless trains.

Prior Knowledge: none
Instructor: Prof. Walter Lewin

#### Magnetic Levitation with Alternating Current

RealVideo®
7:36 minutes (42:04 - 49:40)

Running alternating current through a coil of wire above a conductor. Includes demonstration and levitation of a "woman."

Prior Knowledge: none
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Non-Conservative Fields

PDF
Page 1 to page 3

Explains how Faraday's Law leads to different voltages being measured across the same circuit when a current is induced in the circuit. Includes an example problem.

Prior Knowledge: Non-Conservative Fields (33:42 of video lecture 16)
Instructor: Prof. Walter Lewin

#### Lenz's Law and Faraday's Law

PDF#
Page 2 to page 5

Loops moving in uniform and non-uniform B-fields; induced EMF and Lenz's Law; Faraday's Law.

Prior Knowledge: Ampere's Law
Instructor: Prof. Gabriella Sciolla

#### More on Faraday's Law

PDF#
Page 6 to page 11

General proof of Faraday's Law; applications to dropped and levitating rings; relativity; connection to Maxwell's equations.

Prior Knowledge: Faraday's Law
Instructor: Prof. Gabriella Sciolla

#### Alternating Current and Motors

PDF#
Page 2 to page 4

Creating EMF by changing area, angle, B; alternating current; changing magnitude of B.

Prior Knowledge: Faraday's Law
Instructor: Prof. Gabriella Sciolla

## Online Textbook Chapters

#### Faraday's Law and Lenz's Law

PDF
Page 2 to page 7

Introduction to Faraday's Law for calculating the induced current in an area of changing magnetic flux; includes calculation of flux and use of Lenz's Law to determine the current direction.

Prior Knowledge: Electromotive Force (OT7.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Motional EMF

PDF
Page 7 to page 10

Description of the physical processes which produce an EMF when a conductor moves in a magnetic field.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Induced Electric Field

PDF
Page 10 to page 12

Introduces the concept of a non-conservative induced electric field associated with the induced EMF due to changing magnetic flux.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Electric Generator

PDF
Page 12 to page 13

Illustrative example of an electric generator using a conducting loop rotated in a uniform magnetic field.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Eddy Currents

PDF
Page 14 to page 15

Qualitative description of the eddy currents induced in solid sheets of conductors.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Problem Solving: Faraday's and Lenz's Law

PDF
Page 16 to page 17

Enumerated strategy for keeping the signs straight when solving problems using Faraday's Law and Lenz's Law.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

## Practice Problems

#### Electric Generator

PDF
Problem on page 33 to page 35

For an electric generator composed of a current coil rotating in a uniform magnetic field, find the maximum induced current and the power. Solution is included after problem.

Prior Knowledge: Faraday's Law, Lenz's Law, Power Dissipation in a Resistor
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Induction in a Pie Wedge

PDF
Problem on page 36 to page 39

A conducting bar is free to slide on a circular track in a uniform magnetic field, making a pie-wedge shaped loop; find the force and torque on the bar due to electromagnetic induction. Solution is included after problem.

Prior Knowledge: Lenz's Law, Faraday's Law, Magnetic Force on a Current
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Induction by Increasing Current in an Infinite Wire

PDF
Problem on page 17 to page 19

Find the magnetic flux and induced EMF in a rectangular conducting loop next to an infinite wire with time-varying current. Solution is included after problem.

Prior Knowledge: Faraday's Law (OT10.1), Magnetic Field of an Infinite Current (OT9.1 Ex 9.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Induction by Changing Loop Area

PDF
Problem on page 19 to page 20

Find the average induced current in a conducting loop in a uniform magnetic field as its area is reduced. Solution is included after problem.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Sliding Rod Circuit

PDF
Problem on page 20 to page 21

Find the total power dissipated through two resistors when a conducting rod is pulled along conducting rails in a uniform magnetic field. Solution is included after problem.

Prior Knowledge: Faraday's Law (OT10.1), Electrical Power (OT6.3)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Motional EMF Near an Infinite Wire

PDF
Problem on page 21 to page 22

Find the motional EMF in a conducting rod as it moves away from an infinitely long current-carrying wire. Solution is included after problem.

Prior Knowledge: Motional EMF (OT10.2), Magnetic Field of an Infinite Current (OT9.1 Ex 9.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Induction by Changing Magnetic Field

PDF
Problem on page 22 to page 23

Find the induced EMF, current and power dissipation in a conducting loop perpendicular to a time-varying magnetic field. Solution is included after problem.

Prior Knowledge: Faraday's Law (OT10.1), Electrical Power (OT6.3)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Induction Near an Infinite Wire

PDF
Problem on page 23 to page 24

Find the current in a rectangular conducting loop as it moves away from an infinitely long current-carrying wire. Solution is included after problem.

Prior Knowledge: Faraday's Law (OT10.1), Magnetic Field of an Infinite Current (OT9.1 Ex 9.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Qualitative Induction Questions

PDF
Problem on page 24 to page 25

Qualitatively identify induced electric currents in a conducting loop or shell due to changing magnetic flux.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Sliding Bar with a Battery

PDF
Problem on page 26

Given a conducting bar free to slide on rails in a uniform magnetic field and connected to a battery, show that the bar accelerates to reach a terminal velocity.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Sliding Bar on Wedges

PDF
Problem on page 26 to page 27

Given a conducting bar free to slide on inclined rails in a uniform magnetic field, find the induced current through the bar and compare the mechanical power input to the electrical power dissipated.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### RC Circuit in a Magnetic Field

PDF
Problem on page 27

A conducting loop with a resistor and a capacitor is placed in a time-changing uniform magnetic field; find and describe the maximum charge on the capacitor.

Prior Knowledge: Faraday's Law (OT10.1), RC Circuits (OT7.6)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Rotating Bar in a Magnetic Field

PDF
Problem on page 28

Determine the motional EMF within a bar rotating through a uniform magnetic field.

Prior Knowledge: Motional EMF (OT10.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Rectangular Conducting Loop Pulled Across a Magnetic Field

PDF
Problem on page 28

Find and plot the magnetic flux and induced EMF as a conducting loop is pulled into, through, and out of a region of uniform magnetic field; determine the direction of current flow.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Bar Magnet Pulled Through a Conducting Loop

PDF
Problem on page 29

Qualitatively plot the magnetic flux and induced EMF as a bar magnet is pulled through a conducting loop; discuss the forces on the bar magnet and the source of dissipated energy.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Electric Generator Dimensions

PDF
Problem on page 29 to page 30

Find the magnetic flux and induced EMF as a rectangular conducting loop is rotated in a uniform magnetic field; also calculate dimensions of the loop to tune the voltage produced.

Prior Knowledge: Faraday's Law (OT10.1), Electric Generator (OT10.4)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Plotting Induction in a Time-Varying Magnetic Field

PDF
Problem on page 30 to page 31

Plot the induced EMF, current and power dissipation of a conducting loop in a uniform magnetic field that changes in time as plotted.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Pulling a Square Conducting Loop Across a Magnetic Field

PDF
Problem on page 31

Find the power delivered as an external force pulls a square conducting loop into, through, and out of a region of uniform magnetic field.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Falling Loop in a Magnetic Field

PDF
Problem on page 31 to page 32

Determine the the terminal velocity of a square loop falling due to gravity through a magnetic field and show that the power dissipated is equal to the power from gravity.

Prior Knowledge: Faraday's Law (OT10.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Force on a Loop Moving Near a Magnet

PDF
Problem on page 4

Identify the direction of the force on a wire loop as it moves in the magnetic field of a bar magnet.

Prior Knowledge: Faraday's Law, Lenz's Law, Force on a Current Loop
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Faraday's Law Questions

PDF
Problem on page 1 to page 5

Identify the direction of induced current, force or torque as conducting loops move in magnetic fields.

Prior Knowledge: Faraday's Law, Lenz's Law, Magnetic Field of a Long Wire
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Power Lines

PDF
Problem 2

Why is current transformed to high voltage in power lines?

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

## Exam Questions

#### Voltmeters and Faraday's Law

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Problem 6

Calculating induced EMF and voltmeter reading from a changing magnetic field.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Revolving Conducting Bar

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Problem 7

Finding induced EMF and current for a bar revolving around a circle of wire enclosing a magnetic field.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Electromagnet with Air Gap

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Problem 4

Finding magnetic field strength inside air gap of square electromagnet.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Electric Generator

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Problem 6

Finding maximum AC and power necessary to drive generator.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Changing Magnetic Field in Resistor Circuit

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Problem 13

Finding voltmeter readings and current in a circuit enclosing a changing magnetic field.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Conducting Rail

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Problem 3

Rod sits on rails in B-field; explaining motion of rod with current and without. Solution not included.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

#### Loop Falling Through Magnetic Field

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Problem 3

For loop descending through uniform field, finding dφ/dt, induced current, and velocity.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

#### Melting Iron Nail

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Problem 2

A nail connects a circuit enclosing a charging solenoid; finding power, voltage, and current relationships for the nail.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

## Java Applets

#### The Levitating Ring

Java Applet
Requires Java Virtual Machine

Video animation showing the induced current and magnetic field in a conducting ring that is falling in the magnetic field of a magnet.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Suspended Ring

Java Applet
Requires Java Virtual Machine

Video animation showing the induced current and magnetic field in a conducting ring that is falling underneath the magnetic field of a magnet.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Falling Ring with Finite Resistance

Java Applet
Requires Java Virtual Machine

Video animation showing the induced current and magnetic field in a conducting ring that is falling past a magnet.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Falling Ring with Zero Resistance

Java Applet
Requires Java Virtual Machine

Video animation showing the induced current and magnetic field in a conducting ring that is falling past a magnet.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Levitating Magnet

Java Applet
Requires Java Virtual Machine

Video animations showing the magnetic field around a magnet that is falling towards a conducting ring.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Suspended Magnet

Java Applet
Requires Java Virtual Machine

Video animations showing the magnetic field around a magnet that is falling underneath a conducting ring.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Falling Magnet with a Finite Resistance Ring

Java Applet
Requires Java Virtual Machine

Animated and live video showing the behavior of a magnet falling through a conducting ring.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Falling Magnet with a Zero Resistance Ring

Java Applet
Requires Java Virtual Machine

Video animations showing the magnetic field and behavior of a magnet falling through a conducting ring with zero resistance.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Creating a Magnetic Field

Java Applet
Requires Java Virtual Machine

Video animation showing the creating of a magnetic field by spinning up free charges in a series of five conducting rings.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Destroying a Magnetic Field

Java Applet
Requires Java Virtual Machine

Video animation showing the destruction of a magnetic field by slowing down the free charges in a series of five conducting rings.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Falling Coil Applet

Java Applet
Requires Java Virtual Machine

Interactive applet showing the magnetic field and behavior of a ring falling towards a fixed magnet. The resistance of the ring and strength of the magnetic dipole moment can be varied to affect the behavior of the ring.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Faraday's Law Applet

Java Applet
Requires Java Virtual Machine

Interactive applet in which a conducting ring and a bar magnet can be moved toward or away from one another, leading to an induced current and magnetic field for the ring.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Faraday's Law Applet, Part 2

Java Applet
Requires Java Virtual Machine

Interactive applet showing the induced current and magnetic field when the size and rotation of a conducting ring in a uniform magnetic field are changed.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Falling Magnet Applet

Java Applet
Requires Java Virtual Machine

Interactive applet showing the magnetic field and behavior of a magnet falling towards a conducting ring. The resistance of the ring and strength of the magnetic dipole moment can be varied to affect the behavior of the magnet as it falls.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Magnetic Inductance

Java Applet
Requires Java Virtual Machine

Live video and animations showing the induced current in a conducting ring as a magnet is brought near it.

Prior Knowledge: Faraday's Law (Pages 17-35 of presentation 20)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans