The excess (equal in number) number of electrons that must be placed on each of the two small spheres spaced 3cm apart with a force of repulsion between them to be 10^{-19} \mathrm{~N} is :
A 25
B 225
C 625
D 1250
The excess (equal in number) number of electrons that must be placed on each of the two small spheres spaced 3cm apart with a force of repulsion between them to be 10^{-19} \mathrm{~N} is :
A 25
B 225
C 625
D 1250

Correct option is (C) 625
We need force of repulsion =10^{-19} \mathrm{~N}
Let n no. of increase electrons be placed on each sphere

    \[\begin{array}{l} \Rightarrow \frac{\mathrm{K}(\mathrm{ne})(\mathrm{ne})}{\left(3 \times 10^{-2}\right)^{2}}=10^{-19} \\ \Rightarrow \mathrm{n}^{2} \mathrm{e}^{2}=\frac{10^{-19} \times 9 \times 10^{-4}}{9 \times 10^{9} \times \mathrm{e}^{2}} \\ \Rightarrow \mathrm{n}^{2}=\frac{10^{-32}}{\mathrm{e}^{2}} \Rightarrow \mathrm{n}=\frac{10^{-16}}{e} \end{array}\]

    \[\mathrm{n}=\frac{10^{-16}}{1.6 \times 10^{-19}}\]

    \[\mathrm{n}=\frac{1000}{1.6}=625\]