Question

The energy stored in the electric field produced by a metal sphere is $4.5\, J$. If the sphere contains $ 4 \, \mu C$ charge, its radius will be : [Take : $\frac{1}{4 \pi \epsilon_o } = 9 \times 10^{9} \, N - m^2 / C^2$ ]

• A. 20 mm
• B. 32 mm
• C. 28 mm
• D. 16 mm

Answer 1

Answer: (D)

Energy of sphere = $\frac{Q^{2}}{2C}$
$4.5 = \frac{16\times10^{-12}}{2C}$
$C = \frac{16\times10^{-12}}{9} = 4\pi\varepsilon_{0}R$
$R = \frac{16\times10^{-12}}{9}\times\frac{1}{4\pi\varepsilon_{0}}$
$= 9\times10^{9}\times\frac{16}{9}\times10^{-12}$
$= 16 × 10^{-3} = 16 mm$