Page 296 - Engineering Electromagnetics, 8th Edition

278 ENGINEERING ELECTROMAGNETICS

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 10 years, until he
2
was finally successful in 1831. 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 time-varying magnetic field produces an
electromotive force (emf) that 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 in this section.
Faraday’s law is customarily stated as

d
emf =− V (1)
dt
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 through any and
every surface whose perimeter is the closed path, and d /dt is the time rate of change
of this flux.
A nonzero value of d /dt may result from any of the following situations:

1. A time-changing flux linking a stationary closed path
2. Relative motion between a steady flux and a closed path
3. A combination of the two
The minus sign is an indication that the emf is in such a direction as to produce
a current whose flux, if added to the original flux, would reduce the magnitude of
the emf. This statement that the induced voltage acts to produce an opposing flux is
known as Lenz’s law. 3
If the closed path is that taken by an N-turn filamentary conductor, it is often
sufficiently accurate to consider the turns as coincident and let

d
emf =−N (2)
dt
where is now interpreted as the flux passing through any one of N coincident
paths.

2 Joseph Henry produced similar results at Albany Academy in New York at about the same time.
3 Henri Frederic Emile Lenz was born in Germany but worked in Russia. He published his law in 1834.