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 one sphere to the other during rubbing?

Answer 1

Given:
Force of attraction between the spheres, F = 0.1 N
Separation between the spheres, r = 10⁻² m
By Coulomb's Law, force,  

\[F = \frac{1}{4\pi \epsilon_0}\frac{q_1 q_2}{r^2}\]

Let the no. of electrons transferred from one sphere to the other be n. Then,

\[F = \frac{1}{4\pi \epsilon_0}\frac{\left( nq \right)^2}{r^2}\]

\[\Rightarrow 0 . 1 = \frac{9 \times {10}^{- 9} \times n^2 \times \left( 1 . 6 \times {10}^{- 19} \right)^2}{{10}^{- 4}}\] 

\[ \Rightarrow  \text{n}^2  = \frac{0 . 1 \times {10}^{- 4}}{9 \times {10}^9 \times 1 . 6 \times 1 . 6 \times {10}^{- 38}}\] 

\[ \Rightarrow \text{n} = 2 \times  {10}^{11}\]