Determine the ratio of the electric and gravitational forces between two protons.

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 1.23 × 10^ 36

The electric force between two protons separated by a distance

r

is given by Coulomb's law:

F_e = \dfrac{1}{4\pi\epsilon_0} \dfrac{e^2}{r^2}

The gravitational force between them is given by Newton's law of gravitation:

F_g = G \dfrac{m_p^2}{r^2}

The ratio of the two forces is:

\dfrac{F_e}{F_g} = \dfrac{e^2}{4\pi\epsilon_0 G m_p^2}

Substituting the standard values:

e = 1.6 \times 10^{-19} \text{ C}

\dfrac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2

G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2

m_p = 1.67 \times 10^{-27} \text{ kg}

\dfrac{F_e}{F_g} = \dfrac{9 \times 10^9 \times (1.6 \times 10^{-19})^2}{6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2}

\dfrac{F_e}{F_g} = \dfrac{9 \times 2.56 \times 10^{-29}}{6.67 \times 2.7889 \times 10^{-65}}

\dfrac{F_e}{F_g} = \dfrac{23.04}{18.60} \times 10^{36} \approx 1.23 \times 10^{36}

Determine the ratio of the electric and gravitational forces...