Electrostatics

JEE Main level, single correct, medium

210 of 311

Question 210 of 311

The energy stored in the electric field produced by a metal sphere is 4.5J4.5J. If the sphere contains 4μC4\mu C charge, its radius will be: [Take:14π∈0=9×109Nm2C−2]\left[Take:\dfrac{1}{4\pi {\in }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}\right]

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Answer: (B) 16mm16mm

Energy of sphere =Q22C=\dfrac{{Q}^{2}}{2C}

4.5=16×10−122C4.5=\dfrac{16\times {10}^{-12}}{2C}

C=16×10−129=4πϵ0RC=\dfrac{16\times {10}^{-12}}{9}=4\pi {\epsilon }_{0}R

R=16×10−129×14πϵ0R=\dfrac{16\times {10}^{-12}}{9}\times \dfrac{1}{4\pi {\epsilon }_{0}}

R=16×10−129×14πϵ0R=\dfrac{16\times {10}^{-12}}{9}\times \dfrac{1}{4\pi {\epsilon }_{0}}

=9×109×169×10−12=9\times {10}^{9}\times \dfrac{16}{9}\times {10}^{-12}

=16×10−3=16mm=16\times {10}^{-3}=16mm

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