Question

Two thin spherical shells made of metal are at a large distance apart. One of radius $10cm$ carries a charge of $+0.5\mu C$ and the other of radius $20cm$ 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.
$\frac{k{q}_1}{R_1}=\frac{k{q}_2}{R_2}$
$\Rightarrow q_2=q_1\frac{R_2}{R_1}$
$q_1+q_2=Q_1+Q_2$
$q_1=\frac{R_1}{R_1+R_2}\left(Q_1+Q_2\right)$
$\Rightarrow q_1=\frac{10}{10+20}\left(0.5+0.7\right)=0.4\mu C$
$q_2=\frac{R_2}{R_1+R_2}\left(Q_1+Q_2\right)$
$\Rightarrow q_2=\frac{20}{10+20}\left(0.5+0.7\right)=0.8\mu C$