Question

A cylindrical capacitor consists of two long concentric metalcylinders.If there is a charge of k coulombs per meter on the inside of the cylinder of radius R1, and -k coulombs per meter on the outside cylinder of radius R2,find the electric field E between the cylinders (Gauss law).What is E inside the inner cylinder?Outside the outer cylinder? Find either by inspection or direct integration the potential ɸ such that
E = -  ɸ for each of the three regions above.In each case E is not affected by adding an arbitrary constant to ɸ. Adjust the additive const to make ɸ a continuous func. of space

Answer 1

E= -∇ɸ
This ques. comes under vector analysis, but how to aproach this ques. Pls explain in detail.
its an application oif divergence theorem

Answer 2

by symmetry, E is a function of radius.
now use Gauss's law to integration over a cylinder with radius r:
E(r)*2pi r l=Qenc/e0
E(r)=Qenc/(2 pi r l e0) if r>R1 and 0 if r<R1 or r>R2 (since no net charge is enclosed for r<R1 or r>R2)

Answer 3

(Gauss's law is just the divergence theorem applied to electric fields)

Answer 4

for R2>r>R1, Qenc=k*l, thus
E(r)=k/(2 pi r e0)

Answer 5

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html

Answer 6

Thank you ...the final answer is

Answer 7

when r greater than or equel to R2, how does it works?

Answer 8

when r>=R2, net charge (Qenc)=k*l-k*l=0

Answer 9

the constant term is there so that the potential is continuous

Answer 10

Thank you very much...

Answer 11

glad to have helped :)