Relationship between E and 1/r

1. Oct 12, 2008

degredationz

Hi all,
I was taught that E(field strength) is proportional to 1/r for a setup of a ring(earthed) and a positive electrode(in the centre of the ring).
can anyone confirm this or guide me its derivation?

2. Oct 12, 2008

granpa

think in terms of flux lines. you can see geometrically why the field strength
from a point is r^-2.
from a one dimensional line is r^-1.
from a 2 dimensional sheet is r^0.

3. Oct 12, 2008

degredationz

hi, i do not understand exactly wad you mean... is there any diagram i cud refer to?

4. Oct 12, 2008

granpa

5. Oct 12, 2008

degredationz

oh thanks, it is clearer now.
but how about the part of point vs 1d line vs 2dimentional sheet?

6. Oct 12, 2008

granpa

it should be obvious. visualize it. thats what flux lines are for. start with a 2 dimensional sheet extending to infinity. where are the flux lines going to go? how does their density change as you move away from the sheet?

7. Oct 13, 2008

degredationz

errr, how do i model the ring and a round electrode pressed onto a plane as?
a point charge with a spherical shell? but that will give me E is proportional to 1/r^2. this is the part i do not understand..

8. Oct 13, 2008

HallsofIvy

Staff Emeritus
No, you would model the electrode as the single point, the origin, and the ring as a circle of radius r. Using a spherical shell gives you a 3 dimensional problem so you get 1/r^2 again.

9. Oct 14, 2008

degredationz

oh okay. the theory confused me when it insisted 1/r. i think i gotta clarify with the lab lecturer. i was sure it was 1/r^2 by that understanding. thanks ppl!