Electrostatics: Calculate the Electric Field near a Charged Ring

[polibuda]

Homework Statement

Find the potential at p-point (0,0, z) from a circular ring (x ^ 2 + y ^ 2 = R ^ 2) uniformly charged with linear density q1.

Relevant Equations

q1

I have the problem with my solution. I don't know it is correct. Could somebody check it?

 

[vanhees71]

How can we check without seeing your calculation? Do you have an idea, how to calculate the potential on a given point? Also please use the great LaTeX feature of the forum to make your formulae legible. Just click on "LaTeX Guide" to see how it works:

https://www.physicsforums.com/help/latexhelp/

 

[Delta2]

I guess he/she run into problems uploading the images with his attempt.

...unless what he writes in relevant equations of the OP is his final answer, but we still have to check his work.

 

[polibuda]

I guess he/she run into problems uploading the images with his attempt.

...unless what he writes in relevant equations of the OP is his final answer, but we still have to check his work.

Yes, that is true. I am sorry for my mistakes.

 

[Charles Link]

If you use the approach that $V=-\int \vec{E} \cdot dl$, you would need to integrate from $z'=+\infty$ to $z$. In any case, that method is a lot of extra and unnecessary work. For this problem, you need to simply integrate around the ring of the result of the potential from an infinitesimal segment $ds$ at location $(r,\theta,0)$, (cylindrical coordinates). The total potential from separate charges is additive.