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Coulombs Law
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Mathematical Formulation
The magnitude of the electrostatic force ($\mathbf{F}e$) between two point charges, $q1$ and $q_2$, separated by a distance $r$ in a vacuum, is given by:
$$Fe = ke \frac{|q1 q2|}{r^2}$$ -
Coulombs Law
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where $\hat{\mathbf{r}}{12}$ is the unit vector pointing from $q1$ to $q_2$.
When more than two charges are present, the net electrostatic force on any single charge is the vector sum of the individual forces exerted by all other charges. This is the Principle of Superposition. For a charge $qi$ within a system of $N$ charges, the net force $\mathbf{F}i$ is:
$$\mathbf{F}i = \sum{j=1, j \neq i}^{N} \mathbf{F}_{ji}$$ -
Coulombs Law
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Dependence on Medium
The electrostatic force is significantly attenuated when the charges are embedded within a material medium other than a vacuum. This reduction is quantified by the relative permittivity (or dielectric constant), $\kappa$, of the medium). The force $F$ in a medium is:
$$F = \frac{1}{\kappa} F_{\text{vacuum}}$$ -
Inverse Square Law
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The Inverse-Square Law is a fundamental principle describing how the intensity of a physical quantity, such as radiation, gravity, or electrostatic force, diminishes as the distance from the source of that quantity increases. Mathematically, the intensity ($\text{I}$) is inversely proportional to the square of the distance ($r$) from the point source:
$$\text{I} \propto \frac{1}{r^2}$$ -
Inverse Square Law
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Electromagnetism (Coulomb's Law)
The static electrostatic force ($\text{F}e$) between two point charges ($q1$ and $q_2$) is governed by Coulomb's Law, which exhibits the same inverse-square dependence:
$$\text{F}e = ke \frac{q1 q2}{r^2}$$