Welcome to ECE 3300 at the University of Utah. In Lecture No. 22
we're going to talk about Faraday's and Lenz's law. Faraday's law
is very interesting, because it says that a changing magnetic
field produces an electric field and thus a voltage and a current.
Faraday was considering the case where the current produces the
magnetic field. We've seen this before. Current produces a
magnetic field. It doesn't matter if it's an AC current or a DC
current. And he hypothesized if that's the case then the magnetic
field also ought to produce a current. But this only happens if
there's a variation in time. Lenz's law noted that a changing
magnetic field produces yet another magnetic field that opposes
that change. So let's consider Faraday's experiments. I hope
that you'll take a minute and watch the videos of Faraday's law's
experiments that we've got up on the Internet. So right here
let's just take a loop and let's put a current meter across it so
that we can measure how much current is in this loop. If we have
a magnetic field that is passing through the loop, like so, if
that is changing with time for any reason, then we see a current.
If the magnetic field is static, even if it's there in large, we
won't see this changing, this changing current. So let's consider
three ways that we might change the current going through that
loop. One way is to use a permanent magnet. And move it. There
are several videos of pushing a bar magnet in and out of this
loop. The current meter is only going to be moving while the
magnet is, and as soon as the magnet comes to rest, the current is
going to stop. A second way that we might change the current in
this loop is to set up a second loop. Let's set up one loop right
here like this, which has our current meter on it, and let's set
up another loop or even a set of loops over here with a battery
with a switch so that we can open or close the switch of the
battery. This would produce a current in this loop and thus a
magnetic field going through like this and the magnetic field
would be changing with time when the switch is open or closed.
The magnetic field is going to be picked up in this second loop.
So when the switch is being opened or being closed we'll see a
current in this second loop. So this is magnetic induction. And
that is switching or changing DB by DT. Now a third way that we
can change the amount of magnetic field that is going through this
is have a DC magnetic field but change the loop. So if, for
instance, we were to have a loop with a rod on it, where the rod
could slide in or out over a changing static magnetic field, as
the surface is changing, as the surface that's inside here is
changing, then we would also be seeing current generated in that
loop. Now, there are several important concepts that we need to
understand when we're looking at Faraday's law. One concept is
the concept of magnetic flux. Magnetic flux is just an integral
of the magnetic flux density over a surface. It's an open
surface. Not a closed surface. So let's take the surface of my
loop like this. Suppose that my magnetic flux density is coming
out of the board. I simply add up all the magnetic flux density
that's in this loop. In this case it would be an integral over X
and Y of some magnetic field and that would be the magnetic field
in this Z direction if this were the Z-directed loop dotted with a
Z-directed surface, for example. So flux is telling us the total
magnetic flux density that's passing through that loop. And then
there's another nice thing which is the electromagnetic force
voltage. If we're able to see the current changing, we've got to
assume there's also a voltage across the terminals of this device.
That is found by the number of turns of the loop times the change
of flux with time. Now, remember the change of flux can be
changed by changing the magnetic field or by changing the surface.
