What is the Electric Potential of a Square Loop?

[Shay10825]

Homework Statement

There are four uniformly charged rods of linear charge density $$\lambda$$ and length a, arranged as a square. What is the electric potential a distance z from the center of the square and along the symmetrical axis?

The Attempt at a Solution

http://img813.imageshack.us/i/scan0002s.jpg/

Thanks

 

[G01]

You need to integrate over z:

i.e. Coloumb's law, in this case, should be written in terms of infinitesimal charge elements along the wire:

$$E=\frac{1}{4\pi \epsilon_0}\frac{dq}{r^2}\cos\theta$$

with $dq=\lambda dz$ not $\lambda a$

So, you have to integrate that expression over the length of a side. Other than that your on the right track.

 

[Shay10825]

Is this better?

http://img823.imageshack.us/i/scan0004zg.jpg/