00:01
We have a charge density, linear charge density lambda encased by a cylindrical shell with charge density row from radius a to b.
00:10
We want the electric field in the region less than a between a and b and greater than b.
00:17
When we have the situation where we want the electric field in the region less than a, we can use, as we will use for all three of these parts, gauss's law, which states that e, d.
00:31
Da must be equal to integral of row dv.
00:41
The area enclosed will be after integrating 2 pi r times l, the length of the of the wire.
01:01
This will be equal to lambda times the length of the wire.
01:12
Now if we we divide by over epsilon not.
01:18
If we divide by 2 pi r lambda on both sides, we will get that e, when r is less than a, should be lambda over epsilon, 2 pi r.
01:39
Now this will be in the radial direction, outward in the radial direction.
01:50
Because the lambda is positive, so e will be outward.
01:57
Now we want the electric fields between a and b.
02:04
Again, we use gauces law...