Electric potential at the center of a charged ring

[rgold]

Homework Statement

A wire carrying a charge density of λ=.1c/m is bent into a circle of radius r = 5 cm. What is the electric potential at the center of the circle

Homework Equations

The Attempt at a Solution

λ/2Ԑ₀ is this right? i do not really understand it or where my radius went

 

[Charles Link]

It does appear the potential is $V=Q/(4*\pi*\epsilon_o*r)$ and $Q=2*\pi*r*\lambda$ A more lengthy approach to compute V would be to integrate the electric field from the center to infinity. Anyway, I think you can see how the "r" dropped out. Your answer is correct. The potential from a distribution of charges is the sum of all the potentials from infinitesimal elements of these charges.