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Maxwell's Equations

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So at this point in the semester, where do we stand regarding Maxwell's Equations? Reviewing our work to date, we find that there is only one term remaining for discussion. Today's topic will be Maxwell's modification to Ampere's law by introduction of the concept of displacement current. Conceptually I believe that this is the most difficult aspect of Maxwell's equations to master and frankly it is not that important for computation of magnetic fields as an extension of Ampere's law.

So why are they called Maxwell's equations? The time derivative of the electric flux which enters the fourth equation in conjunction with the time derivative of the magnetic flux in the third equation will result in a partial differential equation (next class!) that we will recognize as the wave equation. So Maxwell contributed the realization that electromagnetic energy propagates as waves with a wave speed with the same value as the speed of light. Light is electromagnetic! Although discussion of the concept of displacement current gets pushed to the end of the semester, it plays a vital role in describing completely the properties of electromagnetism.

Ampere's Law Modified

[long wire]
straight line of current
  [short wire]
straight current segment
length 2a

More to come...

Quiz 10: ac Circuits


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Last updated Dec. 9, 1997.
Copyright George Watson, Univ. of Delaware, 1997.