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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 - Physics

Short Note

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?

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Solution

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,

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

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

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

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

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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 7 Electric Field and Potential
Q 12 | Page 121
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