Two equal positive charges q are on the y axis, one at y = a and the other at y = –a.

(a) Show that the electric field on the x axis is along the x axis with E_x = 2kqx(x² + a²)^–3/2.

(b) Show that near the origin, when x is much smaller than a, E_x is approximately 2kqx/a³.

(c) Show that for values of x much larger than a, E_x is approximately 2kq/x². Explain why you would expect this result even before calculating it.