Potential field created by a hemisphere charged on surface - electrostatic potential - Corrected exercises electromagnetism

Considering a half sphere of center O, of radius R, uniformly charged on surface with the surface density σ.
1. Determine the electrostatic potential at a point M of the axis Oz of symmetry of this hemisphere.
2. Deduce the expression of the electrostatic field at that point Mr.
3. Determine the potential and the electrostatic field on O. ( think for limited development).

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