Maxwell's Equations

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Video Clips

Video RealVideo®
6:03 minutes (44:57 - 51:00)

Statement of all four of Maxwell's Equations in completed form.

Prior Knowledge: Relative Permeability (30:36 of video lecture 21)
Instructor: Prof. Walter Lewin
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Video RealVideo®
1:37 minutes (15:17 - 16:54)

Statement of the second of Maxwell's Equations, that there is no net magnetic flux through a closed surface.

Prior Knowledge: None
Instructor: Prof. Walter Lewin
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Video RealVideo®
9:58 minutes (0:00 - 9:58)

Definition, motivated by trying to find the magnetic field near a charging capacitor using Ampere's Law.

Prior Knowledge: Ampere's Law (beginning of video lecture 15)
Instructor: Prof. Walter Lewin
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Video RealVideo®
4:27 minutes (9:58 - 14:25)

Finding the magnetic field around a charging capacitor using the modified form of Ampere's Law.

Prior Knowledge: Displacement Current (beginning of video lecture 18)
Instructor: Prof. Walter Lewin
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Video RealVideo®
5:10 minutes (14:25 - 19:35)

Using Maxwell-Ampere's Law to find the magnitude of the magnetic field anywhere between the plates of a charging capacitor.

Prior Knowledge: Displacement Current (beginning of video lecture 18)
Instructor: Prof. Walter Lewin
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Video RealVideo®
3:52 minutes (19:35 - 23:27)

Further discussion of Maxwell's discovery of displacement current, as well as his successful prediction of radio waves before their existence was proven by Hertz.

Prior Knowledge: Displacement Current (beginning of video lecture 18)
Instructor: Prof. Walter Lewin
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Practice Problems

Document PDF
Problem 1 to Problem 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 1

How do you know sound is not an EM wave?

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

Document PDF
Page 2 to page 7

Inconsistency in Ampere's Law leads to new term; calculation of displacement current; application to RC circuit; complete Maxwell's Equations.

Prior Knowledge: Faraday's Law
Instructor: Prof. Gabriella Sciolla
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Document PDF
Page 7 to page 10

Solutions of E-field and B-field wave equations in vacuum.

Prior Knowledge: Maxwell's Equations
Instructor: Prof. Gabriella Sciolla
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Document PDF
Page 10 to page 12

Proof that light is an EM wave; connection with SI units; measuring c.

Prior Knowledge: Wave equation solutions
Instructor: Prof. Gabriella Sciolla
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Document PDF
Page 17 to page 35

Statement that a changing magnetic flux induces an EMF. EMF is defined with diagrams. Examples of the ways to induce an EMF: Change B, change A enclosed by the loop, change angle between B and the loop. Link to visualization demonstrating these three cases. Statement of the four Maxwell's equations (almost complete).

Prior Knowledge: Induction (Pages 8-16 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
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Document PDF#
Page 1 to page 7

Definition in terms of a time-changing E field between the plates of a capacitor. Statement of Maxwell-Ampere's Law with the addition of this displacement current.

Prior Knowledge: Ampere's Law (Pages 21-26 of presentation 18)
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 8 to page 10

Statement of Gauss's Law, Faraday's Law, Magnetic Gauss's Law, and the Ampere-Maxwell Law. The Lorentz Force Law is also included.

Prior Knowledge: Gauss's Law (Pages 7-22 of presentation 5), Magnetic Gauss's Law and Lorentz Force (Pages 1-31 of presentation 14), Ampere's Law (Pages 21-26 of presentation 18), and 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
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Document PDF#
Page 4 to page 8

Brief statement of Maxwell's Equations and review of symmetries used for Gauss's Law, Ampere's Law, and Faraday's Law.

Prior Knowledge: Maxwell's Equations (Pages 8-10 of presentation 28)
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

Brief statement of equations for displacement current in E field of a capacitor and the Poynting vector.

Prior Knowledge: Material is from presentation 28.
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 5 to page 13

Statement of all of Maxwell's Equations, plus Lenz's Law and displacement current. Includes diagrams of the symmetries used in applying Gauss's Law and Ampere's Law.

Prior Knowledge: Gauss's Law (Pages 7-22 of presentation 5), Magnetic Gauss's Law and Lorentz Force (Pages 1-31 of presentation 14), Ampere's Law (Pages 21-26 of presentation 18), and 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
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Document PDF
Page 1

Statement of the four Maxwell's Equations.

Prior Knowledge: Gauss's Law (R9), Ampere's Law (R18), and Faraday's Law (R20)
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 1

Maxwell's four equations in complete form.

Prior Knowledge: Maxwell's Equations (44:57 of video lecture 22)
Instructor: Prof. Walter Lewin
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Online Textbook Chapter

Document PDF
Page 3 to page 6

Displacement current motivated and defined; Gauss's Law for magnetism; equations in differential and integral form.

Prior Knowledge: Ampere's Law
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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Exam Questions

Document PDF
Problem 3

4-part problem; finding direction, λ of wave; deciding whether it can be sound or EM.

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