Two metallic spheres of radii 1 cm and 3 cm are given charges of $-1 imes 10^{-2} \mathrm{C}$ and

Question

Two metallic spheres of radii 1 cm and 3 cm are given charges of $-1 	imes 10^{-2} \mathrm{C}$ and $5 	imes 10^{-2} \mathrm{C}$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

Professor PC Thomas Classes · Answer

When the given metallic spheres are connected by a conducting wire, charge will flow till both the spheres acquire a common potential which is given by
$V=\frac{q_{1}+q_{2}}{C_{1}+C_{2}}=\frac{-1 	imes 10^{-2}+5 	imes 10^{-2}}{4 \pi \varepsilon_{0} R_{1}+4 \pi \varepsilon_{0} R_{2}}$
$=\frac{4 	imes 10^{-2}}{4 \pi \varepsilon_{0}\left(1 	imes 10^{-2}+3 	imes 10^{-2}ight)}=\frac{1}{4 \pi \varepsilon_{0}}$
$	herefore \quad$ Final charge on the bigger sphere $=C_{2} V$
$=4 \pi \varepsilon_{0} 	imes 3 	imes 10^{-2} 	imes \frac{1}{4 \pi \varepsilon_{0}}=3 	imes 10^{-2} \mathrm{C}$