Question

Two conducting spheres of radii $5 \,cm$ and $10 \,cm$ 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 \varepsilon_{0} r_{1}+4 \pi \varepsilon_{0} r_{2}}=\frac{Q_{1}+Q_{2}}{4 \pi \varepsilon_{0}\left(r_{1}+r_{2}\right)} $
$=\frac{30 \mu C }{4 \pi \varepsilon_{0}(5+10) \times 10^{-2}}$
$=\frac{30 \times 10^{-6} \times 9 \times 10^{9}}{15 \times 10^{-2}}=18 \times 10^{5} V$
Charge on smaller sphere, $Q_{1}^{\prime}=4 \pi \varepsilon_{0} r_{1} V$
$=\frac{1}{9 \times 10^{9}} \times 5 \times 10^{-2} \times 18 \times 10^{5}$
$=10 \times 10^{-6} C =10\, \mu C$