Question

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

Easy

Solution

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

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