00:01
Here is an example using faraday's law of induction.
00:05
So a reminder about faraday's law.
00:10
Faraday's law says that an emf or voltage is produced in a disconnected wire if there is a changing magnetic flux through the wire.
00:24
With the emf given by minus n, the number of loops in the coil, times, the change in magnetic flux with respect to time.
00:37
So here we're going to be dealing with a single loop, so n equals one.
00:44
A reminder that magnetic flux is a dot product between a magnetic field and an area.
00:54
The magnetic field that we are looking at is directly into the plane of the loop.
01:00
So the dot product just comes out to be b times the area.
01:04
Which for a circular loop is its radius squared times constant pi.
01:14
One thing about the negative in front of faraday's law, that negative goes with lentz's law.
01:21
Lentz law states that the wire will produce a sense of emf that opposes the change that produced the flux for the emf actually.
01:38
And so here are flux.
01:41
We have a magnetic field increasing in time so that the flux into the loop, as seen in the figure, is increasing, which means the induced magnetic field from that loop will be out of the page.
02:02
Using our right -hand rule, we see that we must wrap our fingers of our right hand around the loop with our right hand.
02:11
Our fingers moving to the counterclockwise direction, and then the thumb points out of the page.
02:19
So our induced current will actually be flowing counterclockwise.
02:26
Let's determine how big it is.
02:28
So we are interested in the emf when the magnetic field is a particular value, 1 .33 tesla.
02:42
So that's our first question is, when is the magnetic field equal to 1 .33 tesla, still pointing into the page...