The maximum circumference of an isolated conducting sphere is 2 m. Estimate its capacitance when immersed in water of dielectric constant 81.
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Question

The maximum circumference of an isolated conducting sphere is 2 m. Estimate its capacitance when immersed in water of dielectric constant 81.

G1 Physics · Accepted Answer

2πR=2 m gives R=1/π m. In water, C=4π ε₀ K R = 4 ε₀K ≈ 4×8.85×10⁻¹²×81 ≈ 2.87×10⁻⁹ F = 2870 pF. Nearest option: 2800 pF. Correct answer: D.