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Question: The insulation property of air breaks down at \(E = 3 \times 10^{6}\) volt/metre. The maximum charge...

The insulation property of air breaks down at E=3×106E = 3 \times 10^{6} volt/metre. The maximum charge that can be given to a sphere of diameter 5m5m is approximately (in coulombs)

A

2×10−22 \times 10^{- 2}

B

2×10−32 \times 10^{- 3}

C

2×10−42 \times 10^{- 4}

D

2×10−52 \times 10^{- 5}

Answer

2×10−32 \times 10^{- 3}

Explanation

Solution

E=14πε0×qr2=9×109×qr2E = \frac{1}{4\pi\varepsilon_{0}} \times \frac{q}{r^{2}} = 9 \times 10^{9} \times \frac{q}{r^{2}}

∴ q=E×r29×109=3×106×(2.5)29×109=2.0833×10−3q = \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.