Calculating Charge in a Ring of Charge

[jaejoon89]

For a ring of charge centered about the origin, how would you calculate the charge experienced by a point within the ring of charge but not at the center?
So, I know for a ring of charge dE_x = kdq / r^2 = (k*lambda*ds) / r^2 where ds is the arc length.

Then what do I integrate over?
And does the fact that the point isn't at the center/origin, important?
I'm guessing I need to solve that integral, then determine q.

 

[tiny-tim]

For a ring of charge centered about the origin, how would you calculate the charge experienced by a point within the ring of charge but not at the center?

So, I know for a ring of charge dE_x = kdq / r^2 = (k*lambda*ds) / r^2 where ds is the arc length.

Then what do I integrate over?
And does the fact that the point isn't at the center/origin, important?
I'm guessing I need to solve that integral, then determine q.

Hi jaejoon89!

You integrate over a small arc, of length r dθ, where θ is the angle from the centre of the ring.

 

[jaejoon89]

How do you find the angle from the center of the ring in this case? Here would you just do the angle from the point (it is off center)?

 

[Redbelly98]

θ is the angle around the ring, taken from the center. Integrate over θ from 0 to 2 pi.

You'll also need to figure out r as a function of θ.