Biot-Savart's Law & Ampere's Law

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Video Clips

Video RealVideo®
4:42 minutes (4:44 - 9:26)

Finding the direction of the magnetic field created by a current-carrying wire, with introduction to the right hand rule and a demo of a compass needle responding to the current through a wire.

Prior Knowledge: None
Instructor: Prof. Walter Lewin
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Video RealVideo®
4:27 minutes (12:53 - 17:20)

Forces felt by two parallel current carrying wires, when the currents are in the same or in opposite directions. Includes a demonstration of these forces.

Prior Knowledge: Field of Current-Carrying Wire (4:44 of video lecture 11)
Instructor: Prof. Walter Lewin
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Video RealVideo®
6:25 minutes (8:52 - 15:17)

Finding the magnitude and direction of the magnetic field at the center of a loop of current, with comparison to a dipole field.

Prior Knowledge: Magnetic Field of Current-Carrying Wire (4:44 of video lecture 11)
Instructor: Prof. Walter Lewin
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Video RealVideo®
3:45 minutes (16:54 - 20:39)

Using iron filings to view the magnetic field lines near a current-carrying wire and a loop of current.

Prior Knowledge: Magnetic Field of Current-Carrying Wire (4:44 of video lecture 11) and Magnetic Field of a Current Loop (8:52 of video lecture 14)
Instructor: Prof. Walter Lewin
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Lecture Notes

Document PDF - 1.1 MB
Page 6 to page 15

Magnetic force on a current-carrying wire, with diagrams. Forces felt by wires with parallel and anti-parallel currents, with links to visualizations.

Prior Knowledge: Magnetic Fields and Forces (pages 1-31 of presentation 14)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Document PDF#
Page 24 to page 26

Table of important values and equations for resistors, capacitors, and inductors. Brief review of what happens in RC, RL, LC, and RLC circuits.

Prior Knowledge: Material is from Presentations 10, 12, 24, and 25.
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Document PDF
Page 7 to page 11

Statement; field of current-carrying wire and sheet; units; divergence of B and interpretation.

Prior Knowledge: Magnetic forces
Instructor: Prof. Gabriella Sciolla
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Online Textbook Chapter

Document PDF - 1.9 MB
Page 14 to page 24

Derivation and statement; field of current-carrying cable, current sheet, solenoid, and toroid.

Prior Knowledge: Biot-Savart
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Practice Problems

Document PDF
Page 1 to page 4

Two questions with answers and explanations.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Document PDF
Problem 3

Finding the magnetic field at points outside and in the plane of the ribbon.

Prior Knowledge: None
Instructor: Prof. Walter Lewin
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Document PDF
Problem 1

Explaining in words why parallel currents attract and antiparallel currents repel.

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

Document PDF
Problem 5

Finding magnetic field using geometry from an arrangement of current-carrying wires.

Prior Knowledge: None
Instructor: Prof. Walter Lewin
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Document PDF
Problem 4

Finding field of one loop and force exerted on the other.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland
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Document PDF
Problem 5

Finding field of one loop and force exerted on the other.

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

Java Applet Java Applet
Requires Java Virtual Machine and Shockwave® Player

Applet showing the magnitude and direction of the magnetic field created by a small segment of current.

Prior Knowledge: Magnetic Field of a Current-Carrying Wire (pages 6-15 of LS15)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine and Shockwave® Player

Applet demonstrating the method if integrating around a ring of current to find the magnetic field at a point above the ring.

Prior Knowledge: Magnetic Field of a Ring of Current
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine and Shockwave® Player

Applet showing the magnitude and direction of the magnetic field at any point in or around a ring of current.

Prior Knowledge: Magnetic Field of a Ring of Current
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and behavior of two wires with current flowing in the same direction.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and behavior of two wires with current flowing in different directions.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and attraction of two coaxial wire loops with current flowing in the same direction.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and behavior of two coaxial wire loops with current flowing in different directions.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by a Helmholtz Coil when the two coils have current flowing in the same direction (magnetic dipole moments aligned).

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by a Helmholtz Coil when the two coils have current flowing in different directions (magnetic dipole moments anti-aligned).

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Interactive applet showing the magnetic field created by two rings with variable position, orientation, size, and current.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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Java Applet Java Applet
Requires Java Virtual Machine

Interactive applet simulating the magnetic field and interactions of a current-carrying wire and a compass needle.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
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