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Question: A metallic sphere of radius 18 cm has been given a charge of \(5 \times 10^{- 6}C.\) The energy of t...

A metallic sphere of radius 18 cm has been given a charge of 5×10−6C.5 \times 10^{- 6}C. The energy of the charged conductor is

A

0.2J0.2J

B

0.6J0.6J

C

1.2J1.2J

D

2.4J2.4J

Answer

0.6J0.6J

Explanation

Solution

: Here, r=18cm=18×10−2m,q=5×10−6Cr = 18cm = 18 \times 10^{- 2}m,q = 5 \times 10^{- 6}C

As C=4πεor=18×10−29×109=2×10−11FC = 4\pi\varepsilon_{o}r = \frac{18 \times 10^{- 2}}{9 \times 10^{9}} = 2 \times 10^{- 11}F

Energy of charged conductor is

U=q22C=(5×10−6)2C2×2×10−11F=0.625JU = \frac{q^{2}}{2C} = \frac{(5 \times 10^{- 6})^{2}C}{2 \times 2 \times 10^{- 11}F} = 0.625J