00:02
Okay, so for this one, we have a very long cylinder of an inner radius and outer radius.
00:22
So maybe radius a and radius b.
00:27
On the inside of this guy, we have some line of charge.
00:34
It has lambda equals positive alpha.
00:41
This hollow object also has some linear charge density, equal to positive alpha.
00:56
And the question is, given all of these parameters, find the electric field everywhere.
01:07
So, in order to do that, you first need to write down the galses law.
01:15
A, galses law says that the closed -loop integral of e .da equals the charge that you're looking for inside divided by epsilon 0, we have cylindrical symmetry here and so we get to write down for a flex term right here i'll do that on the right hand side equal e times to pi r r is what distance you are away from your enclosed surface your gaussian surface times l the length along the path that you are going all right what else do we know? we know that in terms of lambda, we can say that q equals alpha times l.
02:28
Remember that lambda equals alpha, charge per length.
02:36
So we can rewrite the electric field as the following.
02:43
Alpha l over epsilon 0 equals e times 2 pi r l and then we get an e equals alpha l over 2 pi r l which just equals alpha alpha x0 which just equals alpha divided by 2 pi r epsilon 0.
03:18
Which is a familiar result.
03:24
And now we want to find the electric field at all regions.
03:30
So here we go, using this result.
03:38
All right.
03:42
For r less than a, we get the following.
03:56
Are less than a, we get that e equals alpha over 2 pi r epsilon zero next region a is less than r less than b and for us a is the inner radius b is the outer radius we get that's the electric field equals zero why is this it's because e equals zero inside conductors and then finally for the region r greater than b the answer is simply that e equals alpha over 2 pi r epsilon 0 plus alpha over 2 pi r epsilon 0 plus alpha over 2 pi r epsilon 0.
05:50
Why is this? well, it's because this is from the inner line, inner line, and this is from the hollow cylinder.
06:16
You have to add them, superposition...