Question

When performing calculations using Coulomb’s Law, why is the force of gravity usually neglected?

Answer 1

The short answer is that the force of gravity is much weaker than electrostatic interactions.

In addition, a difference that appears when calculating is that gravity is always attractive, while the force between charges can be attractive or repulsive.

If we take the two equations we will notice the weakness mentioned above.

Force of gravity

$F_g = \frac{GmM}{r^2}$

Here,

G = Gravitational universal constant

m = Mass of the object

M = Mass of the planet

r = Distance between them

Electrostatic force

$F = \frac{kqQ}{r^2}$

Here,

k = Coulomb's Constant

q = Charge of the object 1

Q = Charge of the object 2

r = Distance between them

The most abundant charges particles are electrons and protons. For protons we have that

$q = 1*10^{-19}C$

$m = 1*10^{-27}kg$

The ratio between them would be given as,

$\frac{F_G}{F_e} = \frac{GmM}{kqQ}$

$\frac{F_G}{F_e} = \frac{(6.67*10^{-11})(1*10^{-27})^2}{(9*10^{9})(1*10^{-19})^2}$

$\frac{F_G}{F_e} \approx 7.411*10^{-37}$

And this ratio is even smaller for electrons.

Therefore the force of gravity compared to the electrostatic force is too small that it can be neglected.