Two metallic spheres of radii 1 , cm and 3 , | vedclass

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(C) When two metallic spheres are connected by a conducting wire,charge flows until both spheres reach a common potential $V$.The total charge $Q_{tot

Vedclass · Accepted Answer

$3 	imes 10^{-2} \, C$

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(C) When two metallic spheres are connected by a conducting wire,charge flows until both spheres reach a common potential $V$.The total charge $Q_{total} = q_1 + q_2 = -1 	imes 10^{-2} + 5 	imes 10^{-2} = 4 	imes 10^{-2} \, C$.The total capacitance $C_{total} = C_1 + C_2 = 4 \pi \varepsilon_0 R_1 + 4 \pi \varepsilon_0 R_2 = 4 \pi \varepsilon_0 (R_1 + R_2)$.The common potential $V = \frac{Q_{total}}{C_{total}} = \frac{4 	imes 10^{-2}}{4 \pi \varepsilon_0 (1 	imes 10^{-2} + 3 	imes 10^{-2})} = \frac{4 	imes 10^{-2}}{4 \pi \varepsilon_0 (4 	imes 10^{-2})} = \frac{1}{4 \pi \varepsilon_0}$.The final charge on the bigger sphere $(R_2 = 3 \, cm)$ is $q_2' = C_2 V = (4 \pi \varepsilon_0 R_2) 	imes V$.$q_2' = (4 \pi \varepsilon_0 	imes 3 	imes 10^{-2}) 	imes \frac{1}{4 \pi \varepsilon_0} = 3 	imes 10^{-2} \, C$.

Two metallic spheres of radii $1 \, cm$ and $3 \, cm$ are given,with charges of $-1 \times 10^{-2} \, C$ and $5 \times 10^{-2} \, C$ respectively. If these are connected by a conducting wire,the final charge on the bigger sphere is

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