Potential for a charged ring and point charge system

[yango_17]

Homework Statement

A ring of radius R lies in the x-y plane with the center at the coordinate origin. The ring is uniformly charged with with a uniform charge density +λ.
a) Charge +q is brought along the z-axis from -∞ to the center of the ring. What is the increase in total potential energy of the system, ΔUa?

Homework Equations

ΔV=-∫E⋅dr
W=qΔV

The Attempt at a Solution

The professor mentioned that the solution is so simple that it doesn't even require us to integrate the electric field in order to find the solution. I'm just confused as to what exactly the electric potential would be at the center of the charged ring. I doubt it'd be zero or ∞, but I'm at a loss as to what else it could be. Any hints to point me in the right direction would be greatly appreciated. Thanks.

 

[blue_leaf77]

You only need to know the electrostatic potential due to a point source.

 

[yango_17]

What does that mean in regards to this situation specifically?

 

[blue_leaf77]

Besides calculating potential through the path integral of electric field, you can also integrate the potential due to point sources consisting the ring. In other words, divide the ring into infinitesimal charge element, use the formula of the electrostatic potential due to a point source, and integrate them over the entire ring.
For a simpler illustration, if you have two charge sitting in the vicinity of each other, then you bring in the third charge from infinity, the change in potential energy will be equal to the sum of energies between third-first and third-second pair of charges. Now extend this idea to a continuous charge distribution forming a circle.