# Coulomb's Law

## Introduction

The effect of the Coulomb force can be well seen in the following experiment. On the left side a negative and a positive metal ball are suspended on threads and on the right side are two negatively charged metal balls are suspended on threads.

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We observe that the negatively-charged metal balls repel each other and negatively-charged and positively-charged metal ball attract each other. This leads to the following conclusion:

Similarly charged bodies repel each other and dissimilar charged attract each other.

### Coulomb's Law

The extent to which two bodies or particles attract or repel depends on the charges and the distance between the bodies / particles. It was discovered in 1785 by Charles Augustin de Coulomb and is:

$$F = \dfrac{1}{4 \pi \cdot \epsilon_0 \cdot \epsilon_r} \cdot \dfrac{Q_1 \cdot Q_2}{r^2}$$ $$\epsilon_0$$ = electric constant, $$\epsilon_r$$ = relative permittivity
$$Q_1, Q_2$$ = Charges of the bodies, $$r$$ = Distance of the centers of mass

The electric constant is the permittivity of free space that is the permeability of the vacuum for electric fields:

$$\epsilon_0 = 8,854 \cdot 10^{-12} \dfrac{A \cdot s}{V \cdot m}$$

The relative permittivity defines the permeability relative to the permittivity of free space (electric constant).

Relative permittivity of some materials:

Material $$\epsilon_r$$ Material $$\epsilon_r$$
Amber 2,8 Polystyrene 2,6
Glass 5 ... 16 Porcelain 4,5 ... 6,5
Synthetic resin bonded paper 3,5 ... 5 Transformer oil 2,5
Sepcial ceramics 100 ... 10.000 Vacuum 1
Air 1,0006 Water 81
Paraffin 2,3

### Sources

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