A charge i is distributed inside a sphere of radius a with density pi(r) that varies with distance r from the center of the sphere. A second spherical charge distribution - charge q2, density P2(r) and radius az, is placed with its center a distance r> (a, +az) from the center of qi. Calculate the force on q exerted by q2.

Let both points charge centered at the center of the sphere.

If the charge density $\rho \left(r\right)$ is constant for a particular r then the charge can be considered as a point charge.

According to Gauss law,

$\oint \overrightarrow{E}.\overrightarrow{dA}=\frac{Q_{enc}}{{\epsilon }_0}$

An electric field will be constant for any point on a sphere of radius r.

An electric field will be constant over dA because of symmetry.

$$\begin{gathered} \oint \overrightarrow{E}.\overrightarrow{dA}=\frac{Q_{enc}}{{\epsilon }_0} \\ E\left(4{\mathrm{\pi r}}^2\right)=\frac{q}{{\epsilon }_0} \\ q=q_1 \end{gathered}$$