Question

Compare the electrostatic force and gravitational force between (1) 2 proton (2) an electron and a proton separated by a distance r

Answer 1

charge on electron = charge on proton = 1.6 × 10^-19 C [ in magnitude ]

mass of electron, m = 9.1 × 10^-31 kg

mass of proton , M = 1.6726 × 10^-27 kg

distance between electron and proton = r

(1) now , gravitational field between two protons,F = GM²/r²
= 6.67 × 10^-11 × (1.6726 × 10^-27)²/r²
= 18.65 × 10^-65/r²

electrostatic force of repulsion acting between two protons , F' = kq²/r²
= 9 × 10^9 × (1.6 × 10^-19)/r²
= 23.04 × 10^-29/r²

so, ratio of electrostatic force and gravitational force = {23.04 × 10^-29/r²}/{18.65 × 10^-65/r²}
= 1.23 × 10^36

(2) now, gravitational force of attraction acting between electron and proton, $F_g$ = GmM/r²

= 6.67 × 10^-11 × (9.1 × 10^-31) × (1.6726 × 10^-27)/r²

= 101.52 × 10^-69/r² ........(1)

electrostatic force of attraction acting between electron and proton, $F_e$ = Kq²/r²

= 9 × 10^9 × (1.6 × 10^-19)²/r²

= 9 × 2.56 × 10^-29/r²

= 23.04 × 10^-29/r² .. .........(2)

now, comparing $F_e$ and $F_g$ :

$\frac{F_e}{F_g}$ ={23.04 × 10^-29/r²}/{101.52 × 10^-69/r²}

= 22.69 × 10^-40

= 2.269 × 10^-39