Question

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

• A. $3\times 10^{-2}C$
• B. $4\times 10^{-2}C$
• C. $1\times 10^{-2}C$
• D. $2\times 10^{-2}C$

Answer 1

Answer: (D)

Radii of sphere $(R_1)=1$ cm = $1\times 10^{-2}$ m ;
$(R_2)=2cm=2\times 10^{-2}$ m and charges on sphere;
$(Q_1)=10^{-2}C$ and $(Q_2)=5\times 10^{-2}$ C.
Common potential (V)
$=\frac{Totalcharge}{Totalcapacity}$
$=\frac{Q_1+Q_2}{C_1+C_2}=\frac{(1\times 10^{-2})+(5\times 10^{-2})}{4\pi {\epsilon }_{0}10^{-2}+4\pi {\epsilon }_0(2\times 10^{-2})}$
= $\frac{6\times 10^{-2}}{4\pi {\epsilon }_0(3\times 10^{-2})}$
Therefore final charge on smaller sphere $(C_{1}V)$ = $4\pi {\epsilon }_0\times 10^{-2}\times \frac{6\times 10^{-2}}{4\pi {\epsilon }_0\times 3\times 10^{-2}}=2\times 10^{-2}$ C.