Question

How far apart must be a proton from a group of 8 protons (held in place next to one another) if the magnitude of the electrostatic force acting on the lone proton due to the group is equal to the magnitude of the gravitational force on the lone proton at Earth's surface/

Answer 1

Answer:

0.33523 m

Explanation:

k = Coulomb constant = $8.99\times 10^{9}\ Nm^2/C^2$

m = Mass of proton = $1.67\times 10^{-27}\ kg$

$q_1=q_2$ = Charge in proton = $1.6\times 10^{-19}\ C$

g = Acceleration due to gravity = 9.81 m/s²

The electric and weight are conserved

$8F_e=W\\\Rightarrow 8\times \dfrac{kq_1q_2}{r^2}=mg\\\Rightarrow r= \sqrt{8\times \dfrac{kq_1q_2}{mg}}\\\Rightarrow r=\sqrt{8\times \dfrac{8.99\times 10^9\times (1.6\times 10^{-19})^2}{1.67\times 10^{-27}\times 9.81}}\\\Rightarrow r=0.33523\ m$

The protons are at a distance of 0.33523 m