Electric Potential Homework: Circle of Radius 5 cm

AI Thread Summary
The discussion focuses on calculating the electric potential at the center of a circular wire with a charge density of λ = 0.1 C/m and a radius of 5 cm. The potential is derived using the formula V = Q/(4πε₀r), where Q is the total charge given by Q = 2πrλ. Participants clarify that the radius does not appear in the final potential expression due to the nature of the charge distribution. A more detailed method involves integrating the electric field from the center to infinity to confirm the results. The consensus is that the initial calculations are correct and the potential can be accurately determined from the charge distribution.
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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
 
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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.
 
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