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Question

(A) When two identical conducting spheres are placed in contact, the total charge is shared equally between them. Initial charge $Q = 4 	imes 10^{-8}

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) When two identical conducting spheres are placed in contact, the total charge is shared equally between them. Initial charge $Q = 4 	imes 10^{-8} 	ext{ C}$. After contact, each sphere has a charge $q = \frac{Q}{2} = \frac{4 	imes 10^{-8}}{2} = 2 	imes 10^{-8} 	ext{ C}$. According to Coulomb's law, the force of repulsion $F$ between them at a distance $r$ is given by: $F = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{q_1 q_2}{r^2}$ Given $F = 9 	imes 10^{-3} 	ext{ N}$ and $\frac{1}{4 \pi \varepsilon_0} = 9 	imes 10^9 	ext{ N m}^2 	ext{ C}^{-2}$. $9 	imes 10^{-3} = \frac{9 	imes 10^9 	imes (2 	imes 10^{-8}) 	imes (2 	imes 10^{-8})}{r^2}$ $r^2 = \frac{9 	imes 10^9 	imes 4 	imes 10^{-16}}{9 	imes 10^{-3}}$ $r^2 = 4 	imes 10^{-4} 	ext{ m}^2$ $r = 2 	imes 10^{-2} 	ext{ m} = 2 	ext{ cm}$.

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