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Two metallic spheres of radii r_{1}\; and\; r_{2}  are separated by a distance ‘d’ as shown in the figure. The capacity of the system is

Option: 1

\frac{4\pi \varepsilon _{0}}{\left ( \frac{r_{1}+r_{2}}{r_{1}r_{2}} \right )-\frac{2}{d}}


Option: 2

\frac{4\pi \varepsilon _{0}}{\left ( \frac{r_{1}+r_{2}}{r_{1}r_{2}} \right )+\frac{2}{d}}


Option: 3

\frac{4\pi \varepsilon _{0}}{\left ( \frac{r_{1}-r_{2}}{r_{1}r_{2}} \right )+\frac{2}{d}}

 


Option: 4

\frac{4\pi \varepsilon _{0}r_{1}r_{2}}{\left ( r_{2}-r_{1} \right )}


Answers (1)

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Answer (1)

V_{1}=\frac{kQ}{r_{1}}-\frac{kQ}{d},V_{2}=\frac{-kQ}{r_{2}}+\frac{kQ}{d}

C=\frac{Q}{V_{1}-V_{2}}=\frac{Q}{\frac{kQ}{r_{1}}+\frac{kQ}{r_{2}}-\frac{2kQ}{d}}=\frac{4\pi \varepsilon _{0}}{\frac{1}{r_{1}}+\frac{1}{r_{2}}-\frac{2}{d}}

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