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

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1. Research of the potential.

  Consider a surface element of the half sphere centered at a point P. The electrostatic potential created at a point M of the axis Oz is expressed as:

By integration over the azimuthal angle and expressing r:

  and :

Can then be expressed:

The potential M is then:

2.Electrostatic field at M
 
  We have :

3. Potential and field on O.

The potential is written in the form:

Calculating the boundary of V where z tends to 0:

For the electric field, the procedure is the same way:

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