7.3.1

# Coulomb's Law

Test yourself

## 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

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

### 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

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

### Gravitational force

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

### Consequences of gravitation force being smaller

• 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.