Page 295 - Engineering Electromagnetics, 8th Edition

9

CHAPTER

Time-Varying Fields

and Maxwell’s Equations

he basic relationships of the electrostatic field and the steady magnetic field
were obtained in the previous eight chapters, and we are now ready to discuss
T time-varying fields. The discussion will be short, for vector analysis and
vector calculus should now be more familiar tools; some of the relationships are
unchanged, and most of the relationships are changed only slightly.
Twonew concepts will be introduced: the electric field produced by a changing
magnetic field and the magnetic field produced by a changing electric field. The first
of these concepts resulted from experimental research by Michael Faraday and the
second from the theoretical efforts of James Clerk Maxwell.
Maxwell actually was inspired by Faraday’s experimental work and by the mental
picture provided through the “lines of force” that Faraday introduced in developing
his theory of electricity and magnetism. He was 40 years younger than Faraday, but
they knew each other during the five years Maxwell spent in London as a young
professor, a few years after Faraday had retired. Maxwell’s theory was developed
subsequent to his holding this university position while he was working alone at his
home in Scotland. It occupied him for five years between the ages of 35 and 40.
The four basic equations of electromagnetic theory presented in this chapter bear
his name. ■

9.1 FARADAY’S LAW
1
After Oersted demonstrated in 1820 that an electric current affected a compass
needle, Faraday professed his belief that if a current could produce a magnetic field,
then a magnetic field should be able to produce a current. The concept of the “field”

1 Hans Christian Oersted was professor of physics at the University of Copenhagen in Denmark.

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