Maxwell's Equations

 

Maxwell's Equations

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

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Lists all of Maxwell's Equations together in both integral and differential forms; also derives the speed of light from Maxwell's Equations in vacuum.

  • 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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Magnetic Gauss's Law

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

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Displacement Current

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

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  • Watch video clip from Lecture 18 (0:00 - 9:58)

Introduces the displacement current in the context of Ampere's Law in a charging capacitor, and states the Ampere-Maxwell 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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Inconsistency in Ampere's Law leads to new term; calculation of displacement current; application to RC circuit; complete Maxwell's Equations.

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Using Displacement Current

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

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  • Watch video clip from Lecture 18 (9:58 - 14:25)

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Magnetic Field Between the Plates of a Capacitor

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

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  • Watch video clip from Lecture 18 (14:25 - 19:35)

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Maxwell and Displacement Current

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.

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  • Watch video clip from Lecture 18 (19:35 - 23:27)

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Maxwell's Equations in Vacuum

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

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1D Electromagnetic Waves

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

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Gauss's Law for Magnetism

States Gauss's Law for magnetic field by analogy with Gauss's Law for electric field, using the non-existence of magnetic monopoles.

  • 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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Cut in a Thick Wire

A thick wire with a narrow cut builds up charge; find the electric and magnetic fields between the ends of the 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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Energy in a Charging Capacitor

Find the electric and magnetic fields over time and the voltage at a point within a charging capacitor; use these to find the total stored 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

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Plane Electromagnetic Wave

Given the electric field of a plane electromagnetic wave, find its propagation direction and the corresponding 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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Conceptual Ampere-Maxwell Questions

Characterize the circulation of magnetic field on an Amperian loop within a charging or discharging 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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EM Plane Wave Questions

Find the electric component of an electromagnetic plane wave consistent with the given magnetic component; and vice versa.

  • 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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Sound Wave

How do you know sound is not an EM wave?

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Plane Wave

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

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