So it turns out that Faraday's law of
induction is actually very important to
our technology. For example, it's how we
do a conversion of energy from
mechanical energy into electrical energy.
Let's look at a schematic version of the
simplest version of one of those devices,
which is an AC generator. So you start
with a magnet or magnets. They produce a permanent magnetic field and then we're
going to put in a coil. That's just a
coil of wire and what we're going to do
is we're going to rotate it around its
axis. And because we've got this area of
coil and we're turning it through the
magnetic field, what that's going to
do is change the magnetic flux that's
going through that coil. The magnetic
fields can be constant, the actual area
of the coil is of course constant, but
the angle is changing and therefore the
perpendicular area is changing. Indeed
it's changing sinusoidally.
So this  A(loop) is the total area of our
loop here but it's changing sinusoidally
because the angle is changing. The
angle is going to go through two pi
radians every time we go through a
period. And so that cosine has to be 2 pi
radians every time we go through a
period, so time divided by period.
So obviously that flux is changing and
so obviously it's going to be time-dependent and therefore it's going to
produce a voltage in that coil. And if
you put many turns on that coil then
you'll get a stronger voltage in that
coil. If we look at the flux as a
function of time:
we start at time equals zero, cos of 0
is 1 and so we start at the maximum of
the magnetic field times the total area
of the loop. And then cos, it just
goes like this. Now if we want to see how
that flux changes in time, we have to
look at the slope of this graph and we
can see that initially it doesn't have
any slope at all and so this will be 0.
So while the coil is in this position
there will be no voltage through the
coil, but then when we get to here we'll
have quite a high slope, and then at this
point we'll have none again, and then a
strong slope going the other way and then
none and so on.
And so we can see at the point where the
slope is the maximum in the negative
direction, we've got a maximum slope
there and when it's flattened out we
have zero change in our magnetic flux.
And then we've got our maximal change
and so on. And of course the change in
the magnetic flux is precisely just
proportional to the voltage. And
therefore this is a picture of the
voltage you're going to get out. If we do
that mathematics properly we'll find
that that's also a sinusoid and you'll
see that it's alternating. And that's why
this is called an AC generator it's also
known as an Alternating Current
generator.
this is actually how all our power is
transmitted in Australia the frequency
at which this is oscillating is 50 Hertz
50 times a second
now some devices don't like the
potential to oscillate like that they're
like a nice constant potential and those
are called direct current devices DC and
to make a DC generator what you do is
you basically take an AC generator and
cheat so all the business end of the
generator with the magnetic fields and
the coils and whatnot is basically the
same but then once these wires come off
here what we can do is we can construct
clever devices that switch which wire
these cords are connected to every half
turn and so what that's going to do is
it's going to take our old alternating
current and it's going to make it look
like this
and there you can see you got a much
flatter looking voltage although it does
have these dips here and the way you can
fix that is you can put in extra coils
so you might have back in your generator
you might have another coil that's at
right-angles and the currents are going
to come out of phase with each other so
they're going to look like this and if
you're really careful you can organize
them to add together such that you get a
very smooth current indeed
