Abstract: Using the superposition principle of the electric field and the methods of theory of elliptic integrals and the mathematic trick, we obtain the electric field distribution in the central axis line generated by an elliptic ring uniformly charged and we make the discussion about it. The important properties of the electric field distribution in the central axis line generated by an elliptic ring uniformly charged are shown.

Key words: uniform charge, elliptic ring, central axis line, field distribution, elliptic integrals