Solution : electric field on the axis of a system (-q, + q) - Corrected exercises of electromagnetism

Electric field on the axis of a (- q + q).
1. Electric field in a point of the axis x'Ox.
The perpendicular plane (P) x'Ox axis and passing through the point O is an antisymmetry plan of distribution of the 2 charges. we have then in a point M' belonging to the x'Ox and the symmetrical of point M of the same axis relative to the plane (P):

we study then the properties of this distribution at a point:

we expresses then the field created by the charges at a point M of the axis x'Ox:

For x> a:

for :

For x = 0 we have:

the function passes an extreme
2. Graphical representation.