Question

Two conducting spheres of radii $3\,cm$ and $1\, cm$ are separated by a distance of $10\,cm$ in free space. If the spheres are charged to same potential of $10\, V$ each, the force of repulsion between them is

• A. $ \left( \frac{1}{3} \right)\times {{10}^{-9}}N $
• B. $ \left( \frac{2}{9} \right)\times {{10}^{-9}}N $
• C. $ \left( \frac{1}{9} \right)\times {{10}^{-9}}N $
• D. $ \left( \frac{4}{3} \right)\times {{10}^{-9}}N $
• E. $ \left( \frac{2}{3} \right)\times {{10}^{-9}}N $

Answer 1

Answer: (A)

$ \frac{K{{q}_{1}}}{3}=10,\frac{K{{q}_{2}}}{1}=10 $
$ K{{q}_{1}}=30\times {{10}^{-2}} $
$ K{{q}_{2}}=10\times {{10}^{-2}} $
$ F=\frac{K{{q}_{1}}{{q}_{2}}}{{{10}^{-2}}} $
$ =\frac{(30\times {{10}^{-2}})(10\times {{10}^{-2}})}{K\times {{10}^{-2}}} $
$ F=\frac{1}{3}\times {{10}^{-9}}N $