The famous author Isaac Asimov once said, “The most exciting
phrase to hear in science, the one that heralds new discoveries, is not
‘Eureka!’ (I found it!) but, ‘That’s funny. …’ ” That might have been what
Faraday thought when he noticed the meter deflection upon connecting and
disconnecting the battery.
According to Faraday’s law, in any closed linear path in
space, when the magnetic flux #
surrounded by the path varies with time, a voltage is induced around the
path equal to the negative rate of change of the flux in webers per second.
V = dp/dt
The minus sign denotes that the direction of the induced
voltage is such as to produce a current opposing the flux. If the flux is
changing at a constant rate, the voltage is numerically equal to the increase
or decrease in webers in 1 s.
The closed linear path (or circuit) is the boundary of a
surface and is a geometric line having length but infinitesimal thickness and
not having branches in parallel.
It can vary in shape or position. If a loop of wire of
negligible cross section occupies the same place and has the same motion as the
path just considered, the voltage will tend to drive a current of electricity
around the wire, and this voltage can be measured by a galvanometer or
voltmeter connected in the loop of wire.
As with the path, the loop of wire is not to have branches
in parallel; if it has, the problem of calculating the voltage shown by an
instrument is more complicated and involves the resistances of the branches.
Even though he didn’t get the result he was looking for in
his earlier experiment— current flowing steadily through the secondary coil —
he did see a hint of current flow in the form of a slight needle deflection in
the galvanometer.
But it was enough to lead him down the right path to the
answer. Eventually, he found that a stationary magnetic field does not induce
current in the secondary coil, but that a changing magnetic field does.
When a battery is first connected to a circuit, the magnetic
field has to build from zero to its maximum. As the field grows, the lines of
flux of the magnetic field cut the turns of wire in the secondary coil, thereby
inducing a current.
Faraday deduced that a changing magnetic field whose lines
of flux cut through a wire will generate a voltage. The value of the voltage is
proportional to the rate of change and the intensity of the magnetic flux. This
is known as Faraday’s law of induction.
According to Faraday’s law of induction, it doesn’t matter
whether the lines of flux are cutting through the wire or the wire is moving
through the lines of flux, as long as they are moving relative to each other.
Therefore, a wire can move through a stationary magnetic field or a magnetic
field can move through a stationary wire and it will still generate voltage.
What is important is that the wire is not moving parallel
relative to the lines of flux (0°), otherwise no lines of flux will be cut and
no voltage will be generated. The movement can, however, be somewhere in
between parallel and perpendicular (90°) relative to each other; then some
lines of flux will be cut and a proportional amount of voltage will be
generated.
For example, if a wire is moving at a 60° angle through a
magnetic field, then it is cutting half as many lines of flux as another wire
traveling at a 90° angle to the magnetic field at the same rate of speed.
Therefore, it would generate half the voltage.
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