Question

Two insulating small spheres are rubbed against each other and placed $1cm$ apart. If they attract each other with a force of $0.1N$, how many electrons were transferred from one sphere to the other during rubbing?

Answer 1

$F=0.1$N

$r=1$cm $={10}^{-2}$(As they rubbed with each other. So the charge on each sphere are equal)

The electrostatic force is given by:

So, $F=\frac{k{q}_1{q}_2}{r^2}$

$\Rightarrow 0.1=\frac{k{q}^2}{({10}^{-2}{)}^2}$

$\Rightarrow q^2=\frac{0.1\times {10}^{-4}}{9\times {10}^9}\Rightarrow q^2=\frac{1}{9}\times {10}^{-14}$

$\Rightarrow q=\frac{1}{3}\times {10}^{-7}$

$1.6\times {10}^{-19}C$ carries by $1$ electron $1C$ carried by $\frac{1}{1.6\times {10}^{-19}}$

$0.33\times {10}^{-7}$c carries by

$\frac{1}{1.6\times {10}^{-19}}\times 0.33\times {10}^{-7}=0.208\times {10}^{12}=2.08\times {10}^{11}$.