Question

# A ring lies in the xy plane, centered at the origin. It has a radius of R and a uniformly distributed total charge Q.What is the potential V(z)?

Trigonometric functions
A ring lies in the xy plane, centered at the origin. It has a radius of R and a uniformly distributed total charge Q. Due to the ring on the z-axis, as a function of z, what is the potential V(z)?

$$\displaystyle{V}{\left({r}\right)}=\frac{{1}}{{{4}\pi{\underset{{{0}}}{{\varepsilon}}}}}\times\frac{{Q}}{{r}}$$ (a)
$$\displaystyle{r}^{{2}}={R}^{{2}}+{z}^{{2}}$$
$$\displaystyle{r}=\sqrt{{{R}^{{2}}+{z}^{{2}}}}$$ (b)
$$\displaystyle{V}{\left({r}\right)}=\frac{{1}}{{{4}\pi{\underset{{{0}}}{{\varepsilon}}}}}\times\frac{{Q}}{{\sqrt{{{R}^{{2}}+{z}^{{2}}}}}}$$