Question

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

Answer 1

Hint: The spheres are insulating, so after rubbing the charge on both the spheres must be equal in magnitude. A charge is a fundamental property of materials. All charged bodies interact with other charged bodies which are a force which is directly proportional to the product of magnitude of charges and inversely proportional to the square of distance between them.

Complete step by step answer:
We know Coulombic force is given by:
\[F=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\]
Where r is the distance between the two charges.
Here r= 0.01 m, F= 0.1 N
Let the number of electrons transferred be n, then
\[F=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{{{(nq)}^{2}}}{{{r}^{2}}}\]
$\Rightarrow 0.1=\dfrac{9\times {{10}^{9}}\times {{n}^{2}}\times {{(1.6\times {{10}^{-19}})}^{2}}}{{{0.01}^{2}}} \\
\Rightarrow {{n}^{2}}=\dfrac{0.1\times {{10}^{-4}}}{9\times {{10}^{9}}\times 1.6\times 1.6\times {{10}^{-38}}} \\
\therefore n=2\times {{10}^{11}} \\ $
So, the number of electrons transferred are \[2\times {{10}^{11}}\].

Additional Information:
To make a neutral body-positive then it has to lose some electrons and if a neutral body is to be made negative then it has to accept some electrons. We should keep in our mind only transfer of negative charge takes place. Protons and neutrons are seated inside the nucleus and they do not move outside it.

Note: Here we had taken the charge to be the charge on the electron because it is the electrons which move from one body to the other. While doing such problems people usually think since there is no actual loss of any mass so mass remains the same but when we see this at atomic scale then there is taking place some loss of mass but it is very low.