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