The electric strength of air is 2.0 x 10⁶ N/C. The largest charge that a metallic sphere of 3 mm radius can hold is

Electric field on the surface of the sphere should not exceed 2.0 x 10⁶ N/C. The electric field on metallic sphere
$=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\times \frac{\mathrm{q}}{{\mathrm{r}}^2}=\left(9\times {10}^9\right)\frac{\mathrm{q}}{{\left(3\times {10}^{-3}\right)}^2}$
Hence $\left(9\times {10}^9\right)\frac{\mathrm{q}}{{\left(3\times {10}^{-3}\right)}^2}=2\cdot 0\times {10}^6$
or     $\mathrm{q}=2\times {10}^{-9}\mathrm{C}=2\mathrm{nC}$