Inductance

Self Inductance

Induced EMF and back EMF in solenoid; self-inductance definition and calculation; energy storage in inductors.

• 8.022 Electricity and Magnetism, Fall 2004
  Prof. Gabriella Sciolla

Course Material Related to This Topic:

• Read lecture notes, pages 5–8

LR Circuits

• 8.02X Physics II: Electricity and Magnetism with an Experimental Focus, Spring 2005
  Dr. Peter Dourmashkin, Prof. Gunther Roland

Course Material Related to This Topic:

Finding current in LR circuit just after opening; graphing current change.

• Complete practice problem 4
• Check solution to practice Problem 4

Mutual Inductance

Definition; reciprocity theorem; transformers.

• 8.022 Electricity and Magnetism, Fall 2004
  Prof. Gabriella Sciolla

Course Material Related to This Topic:

• Read lecture notes, pages 9–11

Introduction of the phenomenon of mutual inductance, whereby the magnetic field produced by one coil induces a current in a nearby coil. Example of two concentric coplanar loops.

• 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

Course Material Related to This Topic:

• Read chapter 11, pages 3–5 of online textbook

RL Circuits

Intuitive RL circuit description; differential equation and solution for charging and discharging; time constant.

• 8.022 Electricity and Magnetism, Fall 2004
  Prof. Gabriella Sciolla

Course Material Related to This Topic:

• Read lecture notes, pages 2–4

Modifies Kirchhoff's Voltage Rule to include the induced EMF due to an inductor, and uses this rule to analyze rising and decaying currents in an RL circuit.

• 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

Course Material Related to This Topic:

• Read chapter 11, pages 15–21 of online textbook

LC Circuits

Oscillation in LC circuits; differential equation and solution; energy conservation.

• 8.022 Electricity and Magnetism, Fall 2004
  Prof. Gabriella Sciolla

Course Material Related to This Topic:

• Read lecture notes, pages 5–6

Description of current oscillations in circuits with inductors and capacitors; includes analogy to harmonic oscillations in a mass-spring system.

• 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

Course Material Related to This Topic:

• Read chapter 11, pages 21–4 of online textbook

In ideal LC circuit, calculating Q(t) and volume of inductor given maximum field.

• 8.02X Physics II: Electricity and Magnetism with an Experimental Focus, Spring 2005
  Dr. Peter Dourmashkin, Prof. Gunther Roland

Course Material Related to This Topic:

• Complete practice problem 3
• Check solution to practice problem 3

Inductors and Self Inductance

Introduces self inductance with examples of a solenoid and a toroid; relates mutual inductance to self inductance.

• 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

Course Material Related to This Topic:

• Read chapter 11, pages 5–9 of online textbook

Energy of the Magnetic Field

Derives the energy stored in an inductor, with an example of an ideal solenoid, and introduces energy density of the 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

Course Material Related to This Topic:

• Read chapter 11, pages 9–15 of online textbook

Problem Solving Strategy: Self Inductance

Enumerated procedure for calculating the self inductance of a loop.

• 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

Course Material Related to This Topic:

• Read chapter 11, pages 38–9 of online textbook

Problem Solving Strategy: Circuits with Inductors

Summary of Kirchoff's Voltage Law for circuits that contain inductors.

• 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

Course Material Related to This Topic:

• Read chapter 11, page 39 of online textbook

Charge in an LC Circuit

Write down equation for charge in an LC circuit, and find the time and stored energies when energy stored in the capacitor reaches its first maximum. 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

Course Material Related to This Topic:

• Complete practice problems on page 40–3

Inductance of a Double-Layer Solenoid

Find the inductance of a wire coiled into the shape of two concentric solenoids. 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

Course Material Related to This Topic:

• Complete practice problems on page 33–5

Magnetic Energy Stored in a Toroid

Find the total energy stored in the magnetic field in a toroid. 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

Course Material Related to This Topic:

• Complete practice problems on pages 39–40

Magnetic Energy in a Wire

Find the total energy stored in the magnetic field in a 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

Course Material Related to This Topic:

• Complete practice problems on page 40–1

Mutual Inductance: Loop and Wire

Find the mutual inductance of a system consisting of a rectangular conducting loop next to a long conducting 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

Course Material Related to This Topic:

• Complete practice problems on page 41–2

Steady-State RL Circuit Current

Find the initial and final currents through each resistor in a two-loop RL circuit. 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

Course Material Related to This Topic:

• Complete practice problems on page 42–3

RL Circuit Dynamics

Find how the current through an inductor evolves in time, for a two-loop RL circuit. 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

Course Material Related to This Topic:

• Complete practice problems on page 43–5

LC Circuit Analysis

Characterize the behavior of an LC oscillator circuit by finding the oscillation frequency, maximum charge, maximum current and total energy. 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

Course Material Related to This Topic:

• Complete practice problems on page 45–7

Conceptual Questions on Inductance

Questions about inductance (1–3), circuits involving inductors (4,6,7).

• 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

Course Material Related to This Topic:

• Complete practice problems on page 47

Inductance of a Solenoid

Find the inductance of a solenoid and the induced EMF when a changing current is applied.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 48

Inductance of a Homemade Solenoid

Find the inductance of a cylindrical coil made by tightly wrapping a length of wire.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 48

Inductors in Series and in Parallel

Show that inductors combine like resistors in series and in parallel; consider the effect of their mutual inductance.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 48–9

RL Circuit with Added Resistance

An additional large resistance is suddenly added in series to a steady-state RL circuit: solve for the current and induced EMF of the inductor as a function of time.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 49

Energy in an RL Circuit

Find the total energy stored and dissipated in an RL circuit when a battery is connected and then, much later, disconnected; estimate the time scale.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 50

Inductance of a Solenoid with an Iron Core

Derive the inductance of a solenoid and then calculate the inductance of the same solenoid when filled with an iron core.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 50–1

RL and LC Circuit

A circuit with two switches is first configured as an RL circuit and then, much later, switched to be an LC oscillator; find the current and energy in the RL circuit and 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

Course Material Related to This Topic:

• Complete practice problems on page 51–2

Electromagnetic Energy in a Spinning Cylindrical Capacitor

Find the magnetic field energy in a spinning charged cylindrical capacitor; also find the electric field energy when the charged cylindrical capacitor is at rest.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 52

Inductance of a Spinning Loop in an External Field

Guided questions to estimate the inductance of a conducting loop spinning like a generator in an external 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

Course Material Related to This Topic:

• Complete practice problems on page 52–3

RL Circuit Questions

Identify the behavior of current as switches close in one- and two-loop RL circuits.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 1–3

Current in a Driven Motor

How does the current in a driven electric motor change when the rotating loop is held still?

• 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

Course Material Related to This Topic:

• Complete practice problems on page 5

LC Circuit Questions

Identify how the charge and current in an LC circuit are behaving at specific moments in the oscillation.

• 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

Course Material Related to This Topic:

• Complete practice problems on page 1–2

Self-inductance and Field Energy

Calculating magnetic field energy and self-inductance of a current-carrying wire.

• 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

Course Material Related to This Topic:

• Complete practice problem 4
• Check solution to practice problem 4

Circuit-Breaking

Explaining the spark from disconnecting circuit; energy stored in L.

• 8.02X Physics II: Electricity and Magnetism with an Experimental Focus, Spring 2005
  Dr.Peter Dourmashkin, Prof. Gunther Roland

Course Material Related to This Topic:

• Complete practice problem 2
• Check solution to practice problem 2

Mutual Inductance of Solenoids

Finding B-fields and mutual inductance of two concentric solenoids.

• 8.02X Physics II: Electricity and Magnetism with an Experimental Focus, Spring 2005
  Dr. Peter Dourmashkin, Prof. Gunther Roland

Course Material Related to This Topic:

• Complete practice problem 1
• Check solution to practice problem 1

LC and RC circuits

Calculating energy stored in LC circuit, Q(t) for capacitor, and energy in inductor; mechanical analogy.

8.02X Physics II: Electricity and Magnetism with an Experimental Focus, Spring 2005
Dr. Peter Dourmashkin, Prof. Gunther Roland

Course Material Related to This Topic:

• Complete practice problem 2
• Check solution to practice problem 2