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

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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

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

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

$2 \times 1 0^{- 6} J$

$4 \times 1 0^{- 7} J$

$3 \times 1 0^{- 6} J$

Solution

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

5×10−7J

2×10−6J

4×10−7J

3×10−6J

The capacitance of spherical capacitor is given as: C=R−r4πϵ∘​Rr​The constant K=4πϵ0​1​=9×109 Farad/mIf R→∞ C=4πϵ∘​rFor r=10 cm; C=9×10−90.1​The energy stored in a capacitor is given as: E=21​CV2E=21​Cv2=21​×910−10​×3002J E=5×10−7J

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A sphere of radius R is having charge Q uniformly distributed over it. The energy density of the electric field in the air, at a distance r(r>R) is given by (in J/m3) :

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A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm. A charge q=20 μ C is given to the inner sphere. Find the heat generated in the process when the inner sphere is connected to the shell by a conducting wire :

A capacitor C1​ is charged to a potential difference V. The charging battery is then removed and the capacitor is connected to an uncharged capacitor C2​. The potential difference across the combination is

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