Question

Each of the two conducting spheres of radius 5 cm and 10 cm is given a charge of $15\mu C$ . After charging the spheres are connected by conducting wire. The charge on the smaller spheres after the connection is equal to.

• A. $7.5\mu C$
• B. $15\mu C$
• C. $10\mu C$
• D. $20\mu C$

Answer 1

Answer: (C)

: Common potential of two spheres $=\frac{Q_1+Q_2}{C_1+C_2}$ $\therefore$ $V=\frac{(15+15)\times {10}^{-6}}{4\pi {\epsilon }_0(5+10)\times {10}^{-2}}$ or $V=\frac{30\times {10}^{-4}}{4\pi {\epsilon }_0\times 15}=\frac{2\times {10}^{-4}}{4\pi {\epsilon }_0}$ $\therefore$ Change on smaller sphere = capacity $\times V$ $q=(4\pi {\epsilon }_0\times 5\times {10}^{-2})\times \frac{2\times {10}^{-4}}{4\pi {\epsilon }_0}C$ $=10\times {10}^{-6}C=10\mu C$