Electric Potential and Field of a Uniformly Charged Ring

[debwaldy]

Homework Statement

derive an expression for the electrical potential at a distance x measured along the axis from the centre of a circular ring of radius R on which a charge Q is uniformly distributed.hence derive an expression for the electric field strength at this point

Homework Equations

to be honest I am not too sure where to go after:
V= -⌠E.dl
any guidance at all would be much appreciated!thanks

The Attempt at a Solution

 

[denverdoc]

It looks like a start, what if the "ring" were simply two charges, each of 1/2Q, and -r,0 and r,0 relative to a test charge at 0,x. What would that look like?

 

[Mr.4]

This simply involves a lil integration.

Q is distributed uniformly throughout the ring. This linear charge denstity on it would be lambda= Q/2pi*R.

Let dV due to each infinitesimally small element (dl) on the ring = (1/4pi*epsilon)*(lambda*dl/(x^2+R^2)^1/2.

Then just integrate from 0 to 2pi*R.

 

[debwaldy]

oh i see, so its ok to treat them as 2 separate point charges and then sum the electric potentials at the end.
doing this i got an expression:
V= - Q/4*pi*ε(x^2 + R^2)^1/2

and E= dV/dx
E = - [Qx]/[4*pi*ε(x^2 + r^2)^3/2]

 

[denverdoc]

no, what i meant was look at it first as 2 point charges, then 4, then an infinite number spread around the ring, but Mr 4 points the way I was hinting at in post above directly.

 

[Mr.4]

Quite so. I think your logic would be more useful in some questions. Thanks for that denverdoc.

 

[denverdoc]

Quite so. I think your logic would be more useful in some questions. Thanks for that denverdoc.

Still getting the hang of helping without doing the work, ie trying to help posters conceptualize w/o telling them how to pursue directly. Sometimes I think I just add to the confusion
J

 

[Mr.4]

Nope. I get you loud and clear! Maybe its coz I'm just as confusing!