Two metallic spheres of radii $1\,cm$ and $2\,cm$ are given charges ${10^{ - 2}}\,C$ and $5 \times {10^{ - 2}}\,C$ respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is
AIPMT 1995, Medium
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(d) ${Q_1} = {10^{ - 2}}C$, ${Q_2} = 5 \times {10^{ - 2}}\,C$
Total charge of the system $ Q = 6 \times {10^{ - 6}}\,C$
Charge on small sphere
$Q{'_1} = \frac{{Q\,{r_1}}}{{{r_1} + {r_2}}} = \frac{{6 \times {{10}^{ - 2}} \times 1}}{{1 + 2}} = 2 \times {10^{ - 2}}\,C$
Total charge of the system $ Q = 6 \times {10^{ - 6}}\,C$
Charge on small sphere
$Q{'_1} = \frac{{Q\,{r_1}}}{{{r_1} + {r_2}}} = \frac{{6 \times {{10}^{ - 2}} \times 1}}{{1 + 2}} = 2 \times {10^{ - 2}}\,C$
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