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Electrostatic & Gravitational Forces

Physics: IB Diploma Higher Level, topic 4.3.5

Comparison of Electrostatic and Gravitational Forces

Coulomb’s Law and Newton’s Law of Gravitation have similar forms but are very different in their magnitudes.

Coulomb force

Coulomb force

  • The Coulomb force between two protons separated by 1.9 × 10-15 m can be found using the formula:
  • F=Qq4πϵ0r2F = \frac{Qq}{4\pi \epsilon_0 r^2}
  • F=(1.6×10−19)24πϵ0(1.9×10−15)2=63.7F = \frac{(1.6\times 10^{-19})^2}{4\pi \epsilon_0 (1.9\times 10^{-15})^2} = 63.7 N
Gravitational force

Gravitational force

  • The gravitational force between the same two protons separated by the same distance is:
  • F=GMmr2F = \frac{GMm}{r^2}
  • F=G(1.67×10−27)(1.67×10−27)(1.9×10−15)2=5.17×10−35F = \frac{G(1.67\times 10^{-27})(1.67\times 10^{-27})}{(1.9\times 10^{-15})^2} = 5.17\times 10^{-35} N
Consequences of gravitation force being smaller

Consequences of gravitation force being smaller

  • The consequences of the attractive gravitational force being considerably smaller in magnitude than the repulsive electrostatic force are profound.
  • This implies that there is another attractive force between two protons (and neutrons) which implies that the strong nuclear force exists.

Test yourself on Electrostatic & Gravitational Forces

  • Which of these statements about the Coulomb electrostatic force and Newton's gravitational force are true?

  • What is the dominant force between two electrons?

  • What is the dominant force between two protons?

  • What is the dominant force between a proton and an electron?

  • The electrostatic repulsion between two protons is much larger than the gravitational attraction between them. What can we conclude about fundamental forces given that nuclei in atoms are stable?

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