Question

Two insulated metal spheres of radii $10cm$ and $15cm$ charged to a potential of $150V$ and $100V$ respectively are connected by means of a metallic wire. What is the charge on the first sphere?

• A. 2 e.s.u.
• B. 4 e.s.u.
• C. 6 e.s.u.
• D. 8 e.s.u.

Answer 1

Answer: (B)

Here, $r_1=10cm,r_2=15cm$
Common potential $V=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$
$=\frac{4\pi {\epsilon }_0\left(r_1{V}_1+r_2{V}_2\right)}{4\pi {\epsilon }_0\left(r_1+r_2\right)}=120$ volt
$q_1=C_{1}V=4\pi {\epsilon }_0{r}_{1}V=\frac{10^{-1}}{9\times 10^9}\times 120C$
$=\frac{12}{9\times 10^9}\times 3\times 10^9$ e.s.u. $=4$ e.s.u.