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Question

Physics Question on Capacitors and Capacitance

The capacitance of a spherical conductor of radius 1 m1 \,m is

A

9×10−9 F9 \times 10^{-9} \, F

B

10 μF10 \,\mu F

C

1.1×10−10 F1.1 \times 10^{-10} \, F

D

1×10−6 F1 \times 10^{-6} \, F

Answer

1.1×10−10 F1.1 \times 10^{-10} \, F

Explanation

Solution

The capacitance of a spherical conductor of radius RR is C=4πε0RC=4\pi\varepsilon_{0}R or C=R14πε0C=\frac{R}{\frac{1}{4\pi\varepsilon_{0}}} Here, R=1 mR=1\,m, 14πε0=9×109 N m2 C−2\frac{1}{4\pi\varepsilon_{0}}=9 \times 10^{9}\,N\,m^{2}\,C^{-2} ∴C=19×109=0.11×10−9 F\therefore C=\frac{1}{9 \times10^{9}}=0.11\times10^{-9}\,F =1.1×10−10 F=1.1 \times10^{-10}\,F