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
$\Rightarrow F=\frac{k{q}^2}{r^2}=0.1$
$\Rightarrow \frac{9\times {\left(10\right)}^9\times {\left(n\times 1.6\times {\left(10\right)}^{-19}\right)}^2}{0.{\left(01\right)}^2}=0.1$
$\Rightarrow \left(n\times 1.6\times {\left(10\right)}^{-19}\right)=\frac{1}{3\times {\left(10\right)}^7}$
$\Rightarrow$ $n=\frac{1}{4.8}\times 10^{12}\approx 2\times 10^{11}$