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CHAPTER
10
TIMEVARYING
FIELDS AND
MAXWELL'S
EQUATIONS
The basic relationships of the electrostatic and the steady magnetic field were
obtained in the previous nine chapters, and we are now ready to discuss time
varying fields. The discussion will be short, for vector analysis and vector calcu
lus should now be more familiar tools; some of the relationships are unchanged,
and most of the relationships are changed only slightly.
Two new 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 5 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 5 years between
the ages of 35 and 40.
The four basic equations of electromagnetic theory presented in this chap
ter bear his name.
322
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View Full Document10.1 FARADAY'S LAW
After Oersted
1
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'' was not available at that time, and Faraday's goal was to show that a
current could be produced by ``magnetism.''
He worked on this problem intermittently over a period of ten years, until
he was finally successful in 1831.
2
He wound two separate windings on an iron
toroid and placed a galvanometer in one circuit and a battery in the other. Upon
closing the battery circuit, he noted a momentary deflection of the galvanometer;
a similar deflection in the opposite direction occurred when the battery was
disconnected. This, of course, was the first experiment he made involving a
changing
magnetic field, and he followed it with a demonstration that either a
moving
magnetic field or a moving coil could also produce a galvanometer
deflection.
In terms of fields, we now say that a timevarying magnetic field produces
an
electromotive force
(emf) which may establish a current in a suitable closed
circuit. An electromotive force is merely a voltage that arises from conductors
moving in a magnetic field or from changing magnetic fields, and we shall define
it below. Faraday's law is customarily stated as
emf
±²
d
±
dt
V
³
1
´
Equation (1) implies a closed path, although not necessarily a closed conducting
path; the closed path, for example, might include a capacitor, or it might be a
purely imaginary line in space. The magnetic flux is that flux which passes
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 Spring '10
 Wilton
 Electromagnet

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