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Coulomb's Law

Physics: AQA A Level, topic 7.3.1

Coulomb's law

Coulomb's law is very similar to Newton's law of gravity except it can both repel and attract objects depending on their charges.

Coulomb's law

Coulomb's law

  • Like charges repel each other, different charges attract each other.
  • Force = constant x charge one x charge two ÷ the distance between them squared
  • F=14πϵ0×Q1Q2r2F=\frac{1}{4{\pi}{{\epsilon}_0}}{\times}\frac{{Q_1}{Q_2}}{r^2}
  • ϵ0{{\epsilon}_0} is the permittivity of free space.
Approximations

Approximations

  • It is far too complex to calculate everything perfectly for charges so we use some approximations to help
  • For a spherical charge, we can consider all of the charge to be at the centre, and so it is a point charge.
  • We can treat air as a vacuum when doing calculations, so there are no interactions bar between the charges.

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 Coulomb's Law

  • What is the correct form of the equation for Coulomb's law?

  • What type of force comes from Coulomb's law?

  • 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?

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