A ring of charge is a smooth idea, but you can get most of the way there with just a few point charges spread evenly around a circle. Start with two, work up to six, and watch the same cancellation happen — the sideways pulls kill each other off and only the axial parts add up.
Choose how many charges to place, from two up to six. Set the ring radius R and how far along the axis the point P sits, either with the sliders or by dragging P directly. Step through four stages. Switch the camera between 3D, top and side.
The total charge stays the same however many charges you use — each one carries Q divided by N, so the ring is always worth the same amount. Step two picks one charge and draws its field at P. Step three splits that into an axial part and a perpendicular part. Step four shows every charge at once, and the perpendicular arrows visibly cancel while the axial ones stack up. The panel shows R, x, and the total field.
All the charges are positive. Values are normalised — k and the total Q are both taken as 1.
You should be able to say why the perpendicular components cancel for any number of charges greater than one, provided they are evenly spaced.