Question

Find the ratio of the electrical and gravitational forces between two protons.

Answer 1

We know that the mass of a proton, m = 1.67 × 10⁻²⁷ kg
Charge on a proton, q = 1.6 × 10⁻¹⁹ C
Gravitational constant, 

\[G = 6 . 67 \times  {10}^{- 11}   N -  \text{m}^2 / {\text{kg}}^2\]

Electrostatic force,

\[F_e  = \frac{1}{4\pi \epsilon_0}\frac{q^2}{r^2}\] 

Gravitational force,

\[F_g  = G\frac{m^2}{r^2}\] 

\[ \Rightarrow \frac{F_e}{F_g} = \frac{q^2}{4\pi \epsilon_0 \text{G m}^2}\] 

\[                         = \frac{9 \times {10}^9 \times \left( 1 . 6 \times {10}^{- 19} \right)^2}{6 . 67 \times {10}^{- 11} \times \left( 1 . 67 \times {10}^{- 27} \right)^2}\] 

\[                         = 1 . 23 \times  {10}^{36}\]