Question

Two insulating small spheres are rubbed against each other and placed $1cm$ apart. Calculate the number of electrons transferred from one sphere to another if they attract each other with a force of $0.1N$ .

• A. $2\times 10^{11}$
• B. $4\times 10^{12}$
• C. $1\times 10^{10}$
• D. $2\times 10^{8}$

Answer 1

Answer: (A)

Let the number of electrons transfered be $n$ .
According to coulomb's law force between two charges is given by,
$F=\frac{k q_{1} q_{2}}{r^{2}}$
hence, the magnitude of force between the given two spheres will be
$\Rightarrow F=\frac{k q^{2}}{r^{2}}=0.1$
$\Rightarrow \frac{9 \times \left(10\right)^{9} \times \left(n \times 1 . 6 \times \left(10\right)^{- 19}\right)^{2}}{0 . \left(01\right)^{2}}=0.1$
$\Rightarrow \left(n \times 1 . 6 \times \left(10\right)^{- 19}\right)=\frac{1}{3 \times \left(10\right)^{7}}$
$\Rightarrow $ $n=\frac{1}{4 . 8}\times 10^{12}\approx2\times 10^{11}$