# Electromagnetic Induction

Course Material Related to This Topic:

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.

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.

## Electric Generators

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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

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.

## Lenz's Law and Faraday's Law

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

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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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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

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## Alternating Current and Motors

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

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## Motional EMF

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Induced Electric Field

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Eddy Currents

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Induction in a Pie Wedge

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Induction by Increasing Current in an Infinite Wire

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Induction by Changing Loop Area

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Sliding Rod Circuit

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Motional EMF Near an Infinite Wire

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Induction by Changing Magnetic Field

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Induction Near an Infinite Wire

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Qualitative Induction Questions

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Sliding Bar with a Battery

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Sliding Bar on Wedges

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## RC Circuit in a Magnetic Field

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Rotating Bar in a Magnetic Field

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Rectangular Conducting Loop Pulled Across a Magnetic Field

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Bar Magnet Pulled Through a Conducting Loop

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Electric Generator Dimensions

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Plotting Induction in a Time-Varying Magnetic Field

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Pulling a Square Conducting Loop Across a Magnetic Field

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Falling Loop in a Magnetic Field

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.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Force on a Loop Moving Near a Magnet

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
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

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## Power Lines

Why is current transformed to high voltage in power lines?

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## Conducting Rail

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

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## Loop Falling Through Magnetic Field

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

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## Melting Iron Nail

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

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## The Levitating Ring

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

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## The Suspended Ring

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

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## The Falling Ring with Finite Resistance

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

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## The Falling Ring with Zero Resistance

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

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## The Levitating Magnet

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

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## The Suspended Magnet

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

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## The Falling Magnet with a Finite Resistance Ring

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

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## The Falling Magnet with a Zero Resistance Ring

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

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## Creating a Magnetic Field

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

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## Destroying a Magnetic Field

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

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## The Falling Coil Applet

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.

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## The Falling Magnet Applet

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.

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## Magnetic Inductance

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

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## Magnet Floating Above a Superconductor

Live video and animation of a small magnet levitating above a superconducting disc.

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