Question

The insulation property of air breaks down at E= 3x 10⁶ volt per metre. The maximum charge that can be given to a sphere of diameter 5 metres is approximately

Easy

Solution

Electric field on the surface of sphere $= \frac{1}{4 {πε}_{0}} \times \frac{q}{r^{2}}$
Its maximum value may be 3 x 10⁶ v/m because after this value, the insulation property of air breaks.
$\begin{aligned} ∴ 3 \times 10^{6} = (9 \times 10^{9}) \times \{q / (2 \cdot 5)^{2}\} \\ q = \frac{(3 \times 10^{6}) (2 \cdot 5)^{2}}{(9 \times 10^{9})} = 2 \times 10^{- 3} C \end{aligned}$

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