Two identical spheres,each carrying a charge | vedclass

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(B) Let $L = 1 \ m$ be the length of the string and $	heta = 30^\circ$ be the angle each string makes with the vertical. The distance $r$ between the

Vedclass · Accepted Answer

$1.8$

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(B) Let $L = 1 \ m$ be the length of the string and $	heta = 30^\circ$ be the angle each string makes with the vertical. The distance $r$ between the two charges is $r = 2L \sin(30^\circ) = 2 	imes 1 	imes 0.5 = 1 \ m$. In equilibrium,the forces acting on one sphere are the tension $T$,the electrostatic force $F_e$,and the gravitational force $mg$. Resolving the tension $T$ into components,we have: $T \sin(30^\circ) = F_e$ $T \cos(30^\circ) = mg$ From the first equation,$T \sin(30^\circ) = \frac{1}{4\pi \varepsilon_0} \frac{Q^2}{r^2}$. Substituting the values: $T 	imes 0.5 = (9 	imes 10^9) 	imes \frac{(10 	imes 10^{-6})^2}{1^2}$ $T 	imes 0.5 = 9 	imes 10^9 	imes 10^{-10} = 0.9$ $T = \frac{0.9}{0.5} = 1.8 \ N$.

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