Question

Two thin spherical shells made of metal are at a large distance apart. One of radius $10 \, cm$ carries a charge of $+0.5 \, \mu C$ and the other of radius $20 \, cm$ carries a charge of $+0.7 \, \mu C$ . The charge on each, when they are connected by a suitable conducting wire is respectively

• A. $0.4$ and $0.8 \, \mu C$
• B. $+0.425$ and $+0.85 \, \mu C$
• C. $+0.5$ and $+0.7 \, \mu C$
• D. $+0.6$ and $+0.6 \, \mu C$

Answer 1

Answer: (A)

Let us assume that the initial charges on the spheres were $Q_{1}$ and $Q_{2}$ respectively and the final charges on the spheres are $q_{1}$ and $q_{2}$ . Finally the potential of both the spheres is the same.
$\frac{k q_{1}}{R_{1}}=\frac{k q_{2}}{R_{2}}$
$\Rightarrow q_{2}=q_{1}\frac{R_{2}}{R_{1}}$
$q_{1}+q_{2}=Q_{1}+Q_{2}$
$q_{1}=\frac{R_{1}}{R_{1} + R_{2}}\left(Q_{1} + Q_{2}\right)$
$\Rightarrow q_{1}=\frac{10}{10 + 20}\left(0 . 5 + 0 . 7\right)=0.4 \, μC$
$q_{2}=\frac{R_{2}}{R_{1} + R_{2}}\left(Q_{1} + Q_{2}\right)$
$\Rightarrow q_{2}=\frac{20}{10 + 20}\left(0 . 5 + 0 . 7\right)=0.8 \, μC$