Solution : Field on the axis of a circular opening of a plane - corrected exercises Gauss theorem


The Load distribution can be seen as the result of the superposition of an infinite plane of a surface density of charge s and a disc with a density - s.
The field at a point M of the axis  according to the principle of superposition is the vector sum of the fields created by each of these distributions taken separately.
  Noting the unit vector normal to the plane and oriented to the point M, z the coast of the point M from the center of the circular opening ,we have , using conventional demonstrated results in progress (demonstrate need to know!):
Finally :