00:01
For this problem, i'm imagining a cylinder x squared plus y screw equals 25.
00:10
So let's this feature the cylinder, so let's see.
00:15
So i'm imagining a cylinder is something like this.
00:18
At the top of the cylinder we have a plane, which is the plane z equals to seventh.
00:26
And the curve here is the curve which is around the cylinder, the intersection, the curve of intersection between the plane and a cylinder.
00:34
So this is c, counterclockwise move from the top, but what i'm looking at is the surface.
00:41
So s is the part of the plane that lies inside the cylinder, that is s.
00:47
S is the part of the plane, z equals 7 that lies inside the cylinder, and the cylinder has equation of expert, was raised when equals to 25.
01:09
So next, we need a normal vector for this plane, and these normals are going to be 0 .8 upwards like this.
01:19
So let's call these unit normals.
01:22
So these unit normals, to be consistent, we'll have to be 0 comma 0 .1.
01:27
These are normal vectors, normal vectors, 2s.
01:33
And since s is part of the plane, that pretty much gives us the vector to be 0 comma 0 .1.
01:41
What about the field? well, in this case, we want to find, to use stokes theorem...