Electric force governs how static electric charges influence each other at a distance. It plays a key role in electrostatics and determines whether particles attract or repel one another. Coulomb’s Law is a mathematical expression that quantifies the electric force between charges, developed based on the experimental findings of Charles-Augustin de Coulomb.
The electric force is the interaction that occurs between any two charged objects. The nature and intensity of the electric force are influenced by both the sign and magnitude of the interacting charges:
This interaction plays a key role in electrostatics, operating along the direct line between the centers of the two charges. Being a vector quantity, it possesses both size and direction.
Based on experimental data, Coulomb found that the force between two stationary point charges is:
By merging these two expressions and incorporating the constant of proportionality, we get:
\( F = k \cdot \frac{q_1 q_2}{r^2} \)
Where \( k \) is the electrostatic constant and in vacuum or free space:
\( k = \frac{1}{4\pi\varepsilon_0} \), with \( varepsilon_0 \approx 8.854 \times 10^{-12} \, {C}^2/{N·m}^2 \)
So the full expression becomes:
\( F = \frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1 q_2}{r^2} \)
When charges are situated within a material medium instead of a vacuum, the electric force between them decreases because of the medium’s dielectric properties. The formula is modified as:
\( F = \frac{1}{4\pi\varepsilon} \cdot \frac{q_1 q_2}{r^2} \)
Here, \( \varepsilon = \varepsilon_r \varepsilon_0 \), where \( \varepsilon_r \) represents the relative permittivity (also known as the dielectric constant) of the surrounding medium.
This gives:
\( F_{medium} = \frac{F_{vacuum}}{\varepsilon_r} \)
To incorporate direction, Coulomb’s law is written in vector form as:
\( \vec{F}_{12} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1 q_2}{r^2} \hat{r}_{21} \)
Where \( hat{r}_{21} \) is the unit vector pointing from charge 1 to charge 2. This vector form helps calculate directionally dependent forces in multiple-charge systems.
In systems involving multiple charges, forces can also be expressed and added using vector components or even matrices in Cartesian coordinates. The components of the force along the x, y, and z axes from multiple charges can be evaluated individually and then assembled using matrix techniques to determine the total force acting on a charge.
The scalar expression for the magnitude of the electric force between two point charges (without considering direction) is as follows:
\( F = \left| \frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1 q_2}{r^2} \right| \)
This magnitude helps in calculating energy, pressure, and motion in electric fields.
In the presence of more than two charges, the net electric force on any single charge is found by adding the individual forces vectorially. This is called the superposition principle:
\( \vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \cdots \)
Coulomb’s law is foundational to understanding electric interactions. It describes how charged particles exert forces on each other and provides tools to compute those forces both in vacuum and within materials. Its vector and scalar forms, and the superposition principle, allow for solving complex problems involving multiple charges in various configurations.
Facebook
Twitter
Linkedin