The energy stored in the electric field produ | vedclass

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(D) The energy stored in a charged spherical conductor is given by $U = \frac{Q^2}{2C}$.Given: $U = 4.5\, J$ and $Q = 4\,\mu C = 4 	imes 10^{-6}\, C$

Vedclass · Accepted Answer

$16$

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(D) The energy stored in a charged spherical conductor is given by $U = \frac{Q^2}{2C}$.Given: $U = 4.5\, J$ and $Q = 4\,\mu C = 4 	imes 10^{-6}\, C$.Substituting the values: $4.5 = \frac{(4 	imes 10^{-6})^2}{2C} = \frac{16 	imes 10^{-12}}{2C}$.$C = \frac{16 	imes 10^{-12}}{9} = 1.77 	imes 10^{-12}\, F$.The capacitance of a spherical conductor is $C = 4\pi\varepsilon_0 R$.Therefore,$R = \frac{C}{4\pi\varepsilon_0} = C 	imes (9 	imes 10^9)$.$R = \frac{16 	imes 10^{-12}}{9} 	imes 9 	imes 10^9 = 16 	imes 10^{-3}\, m$.Converting to millimeters: $R = 16\, mm$.

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.......$mm$. [Take: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\, N\cdot m^2/C^2$]

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