The insulation property of air breaks down at $E = 3 \times 10^{6}$ volt/meter. The maximum charge that can be given to a sphere of diameter $5^{m}$ is approximately (in coulombs)
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$E = \frac{1}{4 \pi \epsilon_0} \times \frac{q}{r^2} = 9 \times 10^9 \times \frac{q}{r^2}$
∴ ∴ $q = \frac{E \times r^{2}}{9 \times 10^{9}} = \frac{3 \times 10^{6} \times (2.5)^{2}}{9 \times 10^{9}} = 2.0833 \times 10^{-3}$
q should be less than 2.0833 × × 10 –3 . In the given set of options 2 × × 10 –3 is the maximum charge which is smaller than 2.0833 × × 10 –3 .
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