Question

Two insulated metal spheres of radii $10 \,cm$ and $15 \,cm$ charged to a potential of $150\, V$ and $100\, V$ 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, $r_{1}=10 \,cm , r_{2}=15\, cm$
Common potential $V=\frac{C_{1} V_{1}+C_{2} V_{2}}{C_{1}+C_{2}}$
$=\frac{4 \pi \varepsilon_{0}\left(r_{1} V_{1}+r_{2} V_{2}\right)}{4 \pi \varepsilon_{0}\left(r_{1}+r_{2}\right)}=120$ volt
$ q_{1} =C_{1} V=4 \pi \varepsilon_{0} r_{1} V=\frac{10^{-1}}{9 \times 10^{9}} \times 120\, C $
$=\frac{12}{9 \times 10^{9}} \times 3 \times 10^{9}$ e.s.u. $=4$ e.s.u.