Uniformly Charged Ring Acting on a Particle

[acedeno]

Homework Statement

Solve for the Electric force exerted on a Particle a distance z above a uniform ring of charge Q.

Determine the potential energy of the charge where the charge lies directly in the center.

Homework Equations

F=kq1q1/r^2

The Attempt at a Solution

Knowing E=F/q I just solved for E then multiplied it by the charge q.

resulting in E=kQz/(z^2+a^2)^3/2 thus, F=kqQz/(z^2+a^2)^3/2

Now, I'm not sure about how to go about expressing the potential energy.
My intuition tells me to do Work=Potential Energy, so,
W= integral of[F(dot)dl]

I'm not sure where to go from here because I'm not sure as to what I should make dl.

 

[ehild]

Potential energy is defined for conservative forces, so as the force is negative gradient of the potential energy. The work of a conservative force when a body moves from point A to B is independent on the path.
You can calculate the potential energy difference by integrating the force along any path form A to B:

$U(B)-U(A) =-\int_{A}^{B}(\vec {F} \cdot \vec{dl} )$

The zero point of the potential energy is arbitrary. In Electrostatics, it is at infinity in most cases. For the path, you can chose the most convenient one. For your problem, it can be along the z axis.

ehild