c
\(E 4 \pi a^{2}=\frac{\int_{0}^{\theta} k r 4 \pi r^{2} d r}{e_{0}}\)

\(E=\frac{k 4 \pi a^{4}}{4 \times 4 \pi \varepsilon_{0}}\)

\(2 \mathrm{Q}=\int_{0}^{\mathrm{R}} \mathrm{kr} 4 \pi \mathrm{r}^{2} \mathrm{dr}\)

\(\mathrm{k}=\frac{2 \mathrm{Q}}{\pi \mathrm{R}^{4}}\)

\(\mathrm{QE}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{QQ}}{(2 \mathrm{a})^{2}}\)

\(\mathrm{R}=\mathrm{a} 8^{1 / 4}\)