For this problem use the results quoted in hw problem 63in...

For this problem use the results quoted in HW Problem 6.3.In both parts, there is no charge in the region between R and 2R. a A conducting sphere of radius R is held at electric potential Vo and is surrounded by a grounded concentric spherical shell of radius 2R. Find the potential V(r) in the intermediate region R< r< 2R. b) An infinitely long conducting cylinder of radius R is held at electric potential V and is surrounded by a grounded concentric cylindrical shell of radius 2R. Find the potential V(s) in the intermediate region R < s < 2R Hint: For part(b),it is easier to write the general form as V(s)= a lns/b.Explain why this is equivalent to A+ Bln(s), but then forget about A and B.

Transcript

00:01 All right, so we have a hollow cylinder that has a length, we call it capital l and a radius of capital r.

00:09 And we want to find what is the electric field at a point, sorry, the cylinder also has a charge key.

00:16 What is the electric field at some point located at a distance lowercase r above the shell? so we're told it's uniformly charged, and so we can use gauss's law here, which says that the electric field, let's draw our gaussian surface to basically be like.

00:31 A cylindrical section that extends a distance little r around our actual cylinder and so we'll have the surface area of the cylinder on the perimeter which is like the perimeter of 2 pi r times the length that's our area of our outer surface this is equal to the charge enclosed by the cylinder which is just q over epsilon knot so our electric field then is going to be q over 2 pi epsilon not and if we look at the value of 1 over 2 pi times epsilon not, this is like twice kulams constant if you think about it, right? this is 1 over 2 pi epsilon not.

01:12 So this is like 1 .7, you know, 9 something times 10 to the 10th.

01:19 And then units will be like newton's times square meters per koum square, but then times q over r times l.

01:26 So this is the answer they get there.

01:29 And then we want to know what is the electric potential at the surface of the cylindrical shell.

01:35 So to do this, we need to know what the potential is inside of the cylinder as well.

01:42 But the electric field inside is going to be zero because there's no charge enclosed in the cylinder.

01:47 So what we can have is our electric potential, let's call it's delta v, but our voltage difference between two points is like the negative line integral of e with respect to r.

01:57 From some initial point to some distance.

02:01 We'll call this r.

02:01 So we'll write an r prime here...

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