Question

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

• A. $ 2 \times 10^{-2} C $
• B. $ 3 \times 10^{-2} C $
• C. $ 4 \times 10^{-2} C $
• D. $ 1 \times 10^{-2} C $

Answer 1

The Correct Option is B

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
Common potential,
$ V = \frac{q_1 + q_2}{C_1 + C_2} = \frac{-1 \times 10^{-2} + 5 \times 10^{-2}}{4\pi \varepsilon_0 R_1 + 4 \pi \varepsilon_0 R_2} $
$= \frac{4\, \times \,10^{-2}}{4\pi \varepsilon_0 (1 \,\times\,10^{-2}+3 \,\times\,10^{-2})}$
$ = \frac{4 \,\times\, 10^{-2}}{4\pi \varepsilon_0\, \times\, 4\, \times \,10^{-2}}\, \, \, ...(i) $
$ \therefore$ Final charge on the bigger sphere is
$ = 4\pi \varepsilon _0\times 3 \times 10^{-2}\times\frac{4\, \times \,10^{-2}}{4\pi \varepsilon_0\, \times \,4 \, \times \,10^{-2}}$ (Using (i))
$ = 3 \times 10^{-2} C $