00:01
Okay, we have a spherical shell with inner radius a and out of radius b, and it's conducting, and it has a charge of minus 3q on it, and then at the center of this shell, we have a charge of plus q.
00:22
It has been placed, and we're asked to find the metric field in three different regions.
00:27
So we're going to use gauss's lock for this.
00:29
So the surface integral of e .da is equal to the enclosed charge divided by a constant epsilon knot.
00:45
So our first area is, let me do this in a different color, to red.
00:55
So our first area is r less than a.
01:01
So here is our gaussian surface, and it's a sphere.
01:10
So we're trying to a gaussian sphere here.
01:18
So when we think about e .da, so it's the electric field dotted with the area vector, which points normal to a surface.
01:33
So, looking at our sphere here, our red sphere, the electric field from that plus q charge is going to be pointing radially outward, right? kind of like that, just in all directions.
01:52
Okay, and the area vector on the sphere will also be pointing radially outward just from this sphere's surface here.
02:08
That means that, oops, that means that, oh man, deleting that an accident.
02:23
So that tells us that e is parallel to da, which means that we can change our integral to eda equals q enclosed over epsilon knot.
02:42
Now, every point on this gaussian surface is going to be the same distance away from that plus q charge.
02:50
This means that the electric field at any point on the surface will be the same.
02:56
So the electric field is constant along the surface, which means we can pull the e out of the integral, and we just get the integral of da, which is 4 pi r squared, or the surface area of a sphere.
03:12
And that equals q enclosed over eptel and not.
03:14
So e equals q enclosed, over the area 4 pi epsilon not times 1 over r squared okay and we're just worried about magnitudes for this problem okay very good let's do part b let's do it in green so now we're looking at a less than r less than b so here is our galsine surface so it's the same thing as part a...