Question

Each of the two conducting spheres of radius 5 cm and 10 cm is given a charge of $ 15\mu C $ . After charging the spheres are connected by conducting wire. The charge on the smaller spheres after the connection is equal to.

• A. $ 7.5\mu C $
• B. $ 15\mu C $
• C. $ 10\mu C $
• D. $ 20\mu C $

Answer 1

Answer: (C)

: Common potential of two spheres $ =\frac{{{Q}_{1}}+{{Q}_{2}}}{{{C}_{1}}+{{C}_{2}}} $ $ \therefore $ $ V=\frac{(15+15)\times {{10}^{-6}}}{4\pi {{\varepsilon }_{0}}(5+10)\times {{10}^{-2}}} $ or $ V=\frac{30\times {{10}^{-4}}}{4\pi {{\varepsilon }_{0}}\times 15}=\frac{2\times {{10}^{-4}}}{4\pi {{\varepsilon }_{0}}} $ $ \therefore $ Change on smaller sphere = capacity $ \times V $ $ q=(4\pi {{\varepsilon }_{0}}\times 5\times {{10}^{-2}})\times \frac{2\times {{10}^{-4}}}{4\pi {{\varepsilon }_{0}}}C $ $ =10\times {{10}^{-6}}C=10\,\mu C $