Search of the direction of the electrostatic field generated by a half-charged sphere surface - Corrected Exercises Gauss Theorem

 

Considering a half sphere of center O, of radius R, uniformly charged surface with the surface density s.

Determine, using only the symmetries The invariance, the Gauss theorem and the superposition principle the direction of the electrostatic field at any point M of the diametrical plane.

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The electric field can thus be defined as the vector translating the action at a distance undergone by a fixed electric charge in a given reference frame from all the other charges, whether they are fixed or mobile. This vector is carried by a line (called the field line) and its direction is towards decreasing potentials. For example, if the field is created by a positive charge and a negative charge, the direction of the electric field vector is towards the negative charge.