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(A) For the particles to be in limiting equilibrium,the electrostatic repulsive force must be equal to the maximum static frictional force.Electrostat

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$12$

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(A) For the particles to be in limiting equilibrium,the electrostatic repulsive force must be equal to the maximum static frictional force.Electrostatic force $F_e = \frac{kq^2}{L^2}$,where $k = 9 	imes 10^9 \, N \cdot m^2/C^2$.Frictional force $F_f = \mu mg$,where $\mu = 0.25$,$m = 10 	imes 10^{-3} \, kg$,and $g = 10 \, m/s^2$.Equating the two: $\frac{kq^2}{L^2} = \mu mg$.$L^2 = \frac{kq^2}{\mu mg} = \frac{(9 	imes 10^9) 	imes (2.0 	imes 10^{-7})^2}{0.25 	imes (10 	imes 10^{-3}) 	imes 10}$.$L^2 = \frac{9 	imes 10^9 	imes 4 	imes 10^{-14}}{0.25 	imes 0.1} = \frac{36 	imes 10^{-5}}{0.025} = \frac{36 	imes 10^{-5}}{25 	imes 10^{-3}} = 1.44 	imes 10^{-2} \, m^2$.$L = \sqrt{1.44 	imes 10^{-2}} = 1.2 	imes 10^{-1} \, m = 0.12 \, m = 12 \, cm$.

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