Question

The energy stored in a sphere of $10$ cm radius when the sphere is charged to a potential difference of $300$ V is

• A. $5\times {10}^{-7}J$
• B. $2\times {10}^{-6}J$
• C. $4\times {10}^{-7}J$
• D. $3\times {10}^{-6}J$

Answer 1

Answer: (A)

$5\times {10}^{-7}J$

The capacitance of spherical capacitor is given as: $C=\frac{4\pi {ϵ}_{\circ }Rr}{R-r}$

The constant $K=\frac{1}{4\pi {ϵ}_0}=9\times {10}^9$ Farad/m

If $R\to \infty$ $C=4\pi {ϵ}_{\circ }r$

For $r=10$ cm; $C=\frac{0.1}{9\times {10}^{-9}}$

The energy stored in a capacitor is given as: $E=\frac{1}{2}C{V}^2$

$E=\frac{1}{2}C{v}^2=\frac{1}{2}\times \frac{{10}^{-10}}{9}\times {300}^{2}J$

$E=5\times {10}^{-7}J$