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Electromagnetic mirrors in the sky: Accessible applications of Maxwell's equations

### Abstract

All too often, Maxwell's equations are taught as mathematical abstractions without any connections to students' personal experiences. However, the interaction of radio waves with Earth's ionosphere provides an opportunity to apply Maxwell's equations in scenarios that have some connections to students' daily lives. A description of how electromagnetic waves propagate through a plasma is derived from Maxwell's equations. This description is used to show how the reflection of radio waves by the ionosphere can be used to enable long range radio communications, to establish that the Sun's emission varies over the solar cycle, and to measure physical properties of the ionosphere.

© 2015 American Association of Physics Teachers

Received 18 November 2014
Accepted 11 February 2015

Acknowledgments:
P.W. acknowledges three anonymous reviewers, funding for ionospheric research from NASA (NNX12AJ39G, NNX14AM21G) and NSF (AST-1211490) and helpful discussions with many colleagues in Boston University's Center for Space Physics.

Article outline:

I. INTRODUCTION
II. PROPAGATION OF AN ELECTROMAGNETIC WAVE THROUGH A PLASMA
A. Maxwell's equations
B. Current density
C. Dispersion relation
D. Interpretation of the dispersion relation
E. Group velocity and phase velocity
F. The magnetic field
G. On starting from Ampere's law or from Faraday's law of induction
III. POTENTIAL APPLICATIONS OF THE DISPERSION RELATION THAT INVOLVE EARTH'S IONOSPHERE
IV. TRANSATLANTIC RADIO COMMUNICATIONS
V. THE INTERACTION OF RADIO WAVES WITH EARTH'S IONOSPHERE
VI. PROVING THE EXISTENCE OF THE IONOSPHERE
VII. SOLAR RADIO NOISE
VIII. SUMMARY

/content/aapt/journal/ajp/83/6/10.1119/1.4913412

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