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  • Two isolated metallic solid sphere of radii R and 2 R are charged such that both of these have same charge density <img alt="\sigma" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Csigma" /

Two isolated metallic solid sphere of radii R and 2 R are charged such that both of these have same charge density \sigma. The sphere are located far away from each other, and connected by thin conducting wire. The new charge density on the bigger sphere.

Option: 1

\frac{40}{3} \pi R^2 \sigma


Option: 2

\frac{20}{5} \pi R^2 \sigma


Option: 3

\frac{5}{3} \frac{R \sigma}{\epsilon_0}


Option: 4

\frac{5}{4} \frac{R \sigma}{E_0}


Answers (1)

best_answer

In this problem After connection, the Common potential -
\mathrm{\begin{aligned} & v=\frac{Q_1+Q_2}{C_1+C_2} \\ & v=\frac{\left[4 \pi R^2+4 \pi(2 R)^2\right] \sigma}{4 \pi \epsilon_0 R+4 \pi \epsilon_0(2 R)} \\ & v=\left[\frac{20 \pi R^2 \sigma}{4 \pi \epsilon_0 R+4 \pi \epsilon_0(2 R)}\right] \\ & v=\frac{20 \pi R^2 \sigma}{12 \pi \epsilon_0 R}=\frac{5}{3} \frac{R \sigma}{\epsilon_0} \end{aligned} }
The new charge on bigger sphere-
\mathrm{\begin{aligned} Q_2^{\prime}=C_2 V & =4 \pi \epsilon_0(2 R) \times\left(\frac{5}{3} \frac{R \sigma}{\epsilon_0}\right) \\ & =\frac{40}{3} \pi R^2 \sigma \quad \text { Ans. } \end{aligned} }
 

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vinayak

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