d
Electric field

\(E=-\frac{d \phi}{d r}=-2 a r.........(i)\)

By Gauss's theorem

\(E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}.........(ii)\)

From \((i)\) and \((ii)\),

\(\mathrm{q}=-8 \pi \varepsilon_{0} a r^{3}\)

\(\Rightarrow \quad d q=-24 \pi \varepsilon_{0} a r^{2} d r\)

Charge density, \(\rho=\frac{d q}{4 \pi r^{2} d r}=-6 \varepsilon_{0} a\)