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2. Electric Potential and Capacitance
hard
The energy stored in the electric field produced by a metal sphere is $4.5\, J$. lf the sphere contains $4\,\mu C$ charge, its radius will be.......$mm$ : [Take : $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N - {m^2}\,/{C^2}\, ]$
A
$20$
B
$32$
C
$28$
D
$16$
(JEE MAIN-2017)
Solution
Energy of sphere $=\frac{Q^{2}}{2 C}$
$4.5=\frac{16 \times 10^{-12}}{2 C}$
$C=\frac{16 \times 10^{-12}}{9}=4 \pi \varepsilon_{0} R$
(capacity of spherical conductor)
$\mathrm{R}=\frac{16 \times 10^{-12}}{9} \times \frac{1}{4 \pi \varepsilon_{0}}$
$\because \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9}$
$=9 \times 10^{9} \times \frac{16}{9} \times 10^{-12}=16\, \mathrm{mm}$
Standard 12
Physics
