Respuesta :
Answer:
The electrostatic force between and electron and a proton is [tex]F=2.30\times 10^{-20}\ N[/tex]
Explanation:
It is given that, charge [tex]q_1[/tex] is placed at a distance [tex]r_o[/tex] from charge [tex]q_2[/tex]. The force acting between charges is given by :
[tex]F=\dfrac{kq_1q_2}{r_o^2}[/tex]
We need to find the force if the distance between them is reduced to [tex]r_o/4[/tex]. It is given by :
[tex]F'=\dfrac{kq_1q_2}{(r_o/4)^2}[/tex]
[tex]F'=16\times \dfrac{kq_1q_2}{r_o^2}[/tex]
[tex]F'=16\times F[/tex]
So, if the the distance between them is reduced to [tex]r_o/4[/tex], the new force becomes 16 times of the previous force.
The electrostatic force between and electron and a proton separated by 0.1 mm or [tex]10^{-4}\ m[/tex] is :
[tex]F=\dfrac{kq_1q_2}{r_o^2}[/tex]
[tex]F=\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{(10^{-4})^2}[/tex]
[tex]F=2.30\times 10^{-20}\ N[/tex]
So, the electrostatic force between and electron and a proton is [tex]F=2.30\times 10^{-20}\ N[/tex]. Hence, this is the required solution.
