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Question
Find the ratio of the electrical and gravitational forces between two protons.
Solution
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,
\[F_g = G\frac{m^2}{r^2}\]
\[ \Rightarrow \frac{F_e}{F_g} = \frac{q^2}{4\pi \epsilon_0 \text{G m}^2}\]
\[ = \frac{9 \times {10}^9 \times \left( 1 . 6 \times {10}^{- 19} \right)^2}{6 . 67 \times {10}^{- 11} \times \left( 1 . 67 \times {10}^{- 27} \right)^2}\]
\[ = 1 . 23 \times {10}^{36}\]
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