Solution Exercise field created by a cone portion

Field created by a portion of a cone.

The planes passing through the axis Ox are the charge distribution of planes of symmetry. The electrostatic field must belong simultaneously to all of these plans therefore their intersection: the field has its direction carried by the axis Ox
Consider a surface element S on the truncated cone centered about the point P.
The figure in the plane of the sheet is as follows:
This surface element creates an elementary field O:

Only the projection of this vector onto axis Ox contributes to the field at the point O:

L is expressed as a function of r:
We get :
The field O is: