Problem

Show that the angle between the isopotential line which passes the point $(r_0,0)$ and the $r$-axis is equal to $\pm 60^\circ$. Calculate the Taylor expansion of the effective potential near the point $(r_0,0)$ and show that to satisfy $\phi(r_0+\Delta r, \Delta z)=\phi(r_0,0)$, $(\Delta z/\Delta r)^2$ must be equal to 3.