Is E Proportional to 1/r for a Ring and Central Electrode Setup?

[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?
thanks in advance!

 

[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.

 

[degredationz]

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.

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

 

[granpa]

http://whatis.techtarget.com/definition/0,,sid9_gci213442,00.html

flux lines can be though of as having a tension along their length and a tendency to repel one another. the field strength at a point is the density of flux lines at that position.

 

[degredationz]

http://whatis.techtarget.com/definition/0,,sid9_gci213442,00.html

flux lines can be though of as having a tension along their length and a tendency to repel one another. the field strength at a point is the density of flux lines at that position.

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

 

[granpa]

it should be obvious. visualize it. that's 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?

 

[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..

 

[HallsofIvy]

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.

 

[degredationz]

http://whatis.techtarget.com/definition/0,,sid9_gci213442,00.html

flux lines can be though of as having a tension along their length and a tendency to repel one another. the field strength at a point is the density of flux lines at that position.

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