### Study of a spherical inhomogeneous distribution - Corrected Exercises Gauss Theorem

Considering in the vacuum a sphere of radius R, the center O, with a volume charge distribution :

and k are constants and

1. Determine the expression of the electrostatic field at any P in space. Note OP = r.
2. Show that within the sphere, the electrostatic field has a maximum for a ratio r / R given.

Calculate the value of k in the case where the field is extremum for r / R = 1/2