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

Question

Verified by Toppr

Answer 1

The capacitance of spherical capacitor is given as: $C = \frac{4 π ϵ _{\circ} R r}{R - r}$
The constant $K = \frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}$ Farad/m
If $R \to \infty$ $C = 4 π ϵ_{\circ} r$
For $r = 10$ cm; $C = \frac{0 . 1}{9 \times 1 0 ^{- 9}}$
The energy stored in a capacitor is given as: $E = \frac{1}{2} C V^{2}$
$E = \frac{1}{2} C v^{2} = \frac{1}{2} \times \frac{1 0 ^{- 10}}{9} \times 30 0^{2} J$

$E = 5 \times 1 0^{- 7} J$

Answer 2

The capacitance of spherical capacitor is given as:

C = \frac{4 π ϵ _{\circ} R r}{R - r}

The constant

K = \frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}

Farad/m

If

R \to \infty

C = 4 π ϵ_{\circ} r

For

r = 10

cm;

C = \frac{0 . 1}{9 \times 1 0 ^{- 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{1 0 ^{- 10}}{9} \times 30 0^{2} J

E = 5 \times 1 0^{- 7} J