An electron revolves around an infinite cylin | vedclass

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(C) The electrostatic force provides the necessary centripetal force for the circular motion of the electron.$F_e = F_c$$eE = \frac{mV^2}{r}$For an in

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(C) The electrostatic force provides the necessary centripetal force for the circular motion of the electron.$F_e = F_c$$eE = \frac{mV^2}{r}$For an infinite line charge,the electric field at a distance $r$ is $E = \frac{2k\lambda}{r}$.Substituting this into the force equation:$e \left( \frac{2k\lambda}{r} ight) = \frac{mV^2}{r}$$V^2 = \frac{e \cdot 2k\lambda}{m}$$V = \sqrt{\frac{e \cdot 2k\lambda}{m}}$Given: $e = 1.6 	imes 10^{-19} \, C$,$k = 9 	imes 10^9 \, N \cdot m^2 \cdot C^{-2}$,$\lambda = 2 	imes 10^{-8} \, C \cdot m^{-1}$,$m = 9 	imes 10^{-31} \, kg$.$V = \sqrt{\frac{1.6 	imes 10^{-19} 	imes 2 	imes 9 	imes 10^9 	imes 2 	imes 10^{-8}}{9 	imes 10^{-31}}}$$V = \sqrt{\frac{1.6 	imes 10^{-19} 	imes 36 	imes 10^1}{9 	imes 10^{-31}}}$$V = \sqrt{6.4 	imes 10^{13} 	imes 10^{-18} 	imes 10^{31}}$$V = \sqrt{64 	imes 10^{12}} = 8 	imes 10^6 \, m \cdot s^{-1}$.Thus,the velocity is $8 	imes 10^6 \, m \cdot s^{-1}$.

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