Question

Two conducting spheres of radii $5cm$ and $10cm$ are given a charge of $15\mu C$ each. After connecting the spheres by a copper wire, the charge on the smaller sphere is equal to

• A. $20\mu C$
• B. $5\mu C$
• C. $10\mu C$
• D. $15\mu C$

Answer 1

Answer: (C)

Common potential, $V=\frac{Q_1+Q_2}{C_1+C_2}$
$V=\frac{Q_1+Q_2}{4\pi {\epsilon }_0{r}_1+4\pi {\epsilon }_0{r}_2}=\frac{Q_1+Q_2}{4\pi {\epsilon }_0\left(r_1+r_2\right)}$
$=\frac{30\mu C}{4\pi {\epsilon }_0(5+10)\times 10^{-2}}$
$=\frac{30\times 10^{-6}\times 9\times 10^9}{15\times 10^{-2}}=18\times 10^{5}V$
Charge on smaller sphere, $Q_1^{\prime }=4\pi {\epsilon }_0{r}_{1}V$
$=\frac{1}{9\times 10^9}\times 5\times 10^{-2}\times 18\times 10^5$
$=10\times 10^{-6}C=10\mu C$