Question 21:
easy
The electric field in a region is directed outward and is proportional to the distance \(r\) from the origin. If we take a spherical volume of radius \(r\) taking centre at the origin, then the charge contained inside the volume is proportional to
From Gauss's Law, the enclosed charge is proportional to the electric flux: \(q \propto E \cdot A\). Since \(E \propto r\) and area \(A \propto r^2\), we get \(q \propto r \cdot r^2 = r^3\).