Solution : Field on a spherical cavity - Corrected Exercises Gauss Theorem

 

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We Can modeled within a cavity hollowed out of the sphere R as the superposition of a charged sphere of radius a volume density - ρ   of center O2 and a full sphere of volume density ρ of radius R and center O1.

The principle of superposition is applied at a point M of the cavity:

field created by the distribution ρ

field created by the distribution - ρ

Symmetry and invariance of each source can be concluded for each radial field :

Using the Gauss, taking for each distribution a sphere of radius r and center Oi closed surface and passing through the point M.

  We get :

The field is uniform at any point inside the cavity.

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