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Ratio of gravitational force to the electrostatic force between one proton and one electron separated by certain distance is

Ratio of gravitational force to the electrostatic force between one proton and one electron separated by certain distance is

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Let R be the distance between the electron and the proton 

According to Newton's law of gravity the magnitude of the gravitational force between them is given by: 
Fg = G∙me∙mp/R² 

Electron as well as proton carry single elementary charge 
|q| = e = 1.602∙10⁻¹⁹C 
According to Coulomb's law the magnitude of electrostatic force between them is given by: 
Fg = k∙e²/R² 

Therefore 
Fe/Fg = (k∙e²/R²) / (G∙me∙mp/R²) 
= (k∙e²) / (G∙me∙mp) 
= (8.99∙10⁹Nm²/C² ∙ (1.602∙10⁻¹⁹C)² ) / ( 6.672∙10⁻¹¹Nm²/kg ∙ 9.109∙10⁻³¹kg ∙ 1.672∙10⁻²⁷kg ) 
= 2.27∙10³⁹

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