Find the electrostatic potential above loop of charge Q?

[Poirot]

Homework Statement

An electric charge Q is uniformly distributed along a thin circular wire situated in the z = 0 plane at x² + y² = R² . Determine the electrostatic potential at the point (0, 0, D).

Homework Equations

The Attempt at a Solution

I figured the only components that mattered would be the one perpendicular to the wire since the parallel components would cancel with the other side of the wire. But I'm not sure what equation to use, or how to approach this. I also found tan of the angle between the point and the loop is R/D, not sure if I need that?

Thanks in advance.

 

[TSny]

Keep in mind that electrostatic potential is not a vector quantity. So, there are no components. You'll need to know the formula for the potential of a point charge. Break the circular ring into infinitesimal bits of charge, each bit acts like a point charge.

 

[Klause]

So potential due to a continuous distribution of charge : V= 1/(4πε₀)∫dq/r

Where r is the distance of the wire to the point at which you are trying to find the potential. In this case, D.
So since the wire has a radius R. The r=√(R²+D). This is because all points along the ring are at the same distance from the point at (0,0,D).

So then plugging this into the first equation, do you notice anything interesting? Perhaps a constant you can factor out leaving you with an easy integral.

 

[Poirot]

Thanks for the help, figured it out now. :)