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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 Tue Nov 18 00:00:00 UTC 2014
Accepted Wed Feb 11 00:00:00 UTC 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

1.

1. D. J. Griffiths, Introduction to Electrodynamics, 4th ed. ( Pearson, Boston, 2013).

2.

2. W. J. Duffin, Advanced Electricity and Magnetism for Undergraduates ( McGraw-Hill, London, 1968).

3.

3. J. D. Jackson, Classical Electrodynamics, 2nd ed. ( Wiley, New York, 1975).

4.

4. P. Lorrain, D. P. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. ( W. H. Freeman, New York, 1988).

5.

5. G. R. Fowles, Introduction to Modern Optics, 2nd ed. ( Dover, New York, 1975).

6.

6. E. Hecht, Optics, 4th ed. ( Addison-Wesley, Reading, Mass., 2002).

7.

7. F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 3rd ed. ( Pearson Prentice-Hall, New Jersey, 2007).

8.

8. F. S. Crawford, Waves (Berkeley Physics Course—Volume 3) ( McGraw-Hill, New York, 1968).

9.

9. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics ( Addison-Wesley, New York, 1964), Vol. II.

10.

10. F. Read, Electromagnetic Radiation (The Manchester Physics Series) ( Wiley, New York, 1980).

11.

11. M. Born and E. Wolf, Principles of Optics ( Cambridge U.P., New York, 1999).

12.

12. T. Freegarde, Introduction to the Physics of Waves ( Cambridge U.P., New York, 2012).

13.

13. A. P. French, Special Relativity ( Cambridge U.P., New York, 1968).

14.

14. K. G. Budden, The Propagation of Radio Waves ( Cambridge U.P., New York, 1985).

15.

15. S. J. Bauer and H. Lammer, Planetary Aeronomy ( Springer, New York, 2004).

16.

16. M. H. Rees, Physics and Chemistry of the Upper Atmosphere ( Cambridge U.P., New York, 1989).

17.

17. R. W. Schunk and A. F. Nagy, Ionospheres, 2nd ed. ( Cambridge U.P., New York, 2009).

18.

18. C.-P. Yang, Probing the Sky With Radio Waves ( University of Chicago Press, Chicago, 2013).

19.

19. A. E. Kennelly, “ On the elevation of the electrically-conducting strata of the Earth's atmosphere,” Electr. World Eng. 39, 473–473 (1902).

20.

20. O. Heaviside, “ The theory of electric telegraphy” in Encylopedia Britannica, 10th ed. ( A&C Black London, 1902), Vol. 33, pp. 215–215.

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