Solution Exercise field created by a cone portion

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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:

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