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Coulomb’s law for electrostatic force between two point charges and Newton’s law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges/masses. Compare the strength of these forces by determining the ratio of their magnitudes for two protons. $(mp = 1.67 × 10^{–27}\; kg, m_e = 9.11 × 10^{–31}\; kg)$

1 Answer

On similar lines, the ratio of the magnitudes of electric force to the gravitational force between two protons at a distance r apart is
$\bigg| \large\frac{Fe}{F_G} \bigg| = \frac{e^2}{4 \pi \in_0 G m_p m_e} $$
$\qquad= 1.3 \times 10^{36}$
However, it may be mentioned here that the signs of the two forces are different. For two protons, the gravitational force is attractive in nature and the Coulomb force is repulsive. The actual values of these forces between two protons inside a nucleus (distance between two protons is $\sim 10^{-15}$ m inside a nucleus) are $F_e \sim 1.9 \times 10^{-34} N$
The (dimensionless) ratio of the two forces shows that electrical forces are enormously stronger than the gravitational forces
answered May 29, 2014 by meena.p

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