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(C) The capacitance of a spherical conductor is given by $C = 4\pi \varepsilon_0 R$.Given diameter $d = 10^{-3} \ m$,so radius $R = 0.5 	imes 10^{-3}

Vedclass · Accepted Answer

$6.95$

Vedclass · Answer

(C) The capacitance of a spherical conductor is given by $C = 4\pi \varepsilon_0 R$.Given diameter $d = 10^{-3} \ m$,so radius $R = 0.5 	imes 10^{-3} \ m$.$C = \frac{0.5 	imes 10^{-3}}{9 	imes 10^9} = \frac{1}{18} 	imes 10^{-12} \ F$.The rate of charge emission from the surface is $I = 0.80 	imes (6.25 	imes 10^{10}) 	imes (1.6 	imes 10^{-19}) \ C/s$.$I = 0.80 	imes 10 	imes 10^{-9} = 8 	imes 10^{-9} \ C/s$.Using $q = CV$,where $q = I 	imes t$:$(8 	imes 10^{-9}) 	imes t = (\frac{1}{18} 	imes 10^{-12}) 	imes 1.0$.$t = \frac{10^{-12}}{8 	imes 10^{-9} 	imes 18} = \frac{10^{-3}}{144} \approx 6.944 	imes 10^{-6} \ s = 6.944 \ \mu s$.Rounding to the nearest option,$t \approx 6.95 \ \mu s$.

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