Coulomb’s Law

​Coulomb measured the force of attraction and repulsion between two stationary charges by using a torsion balance. His observations are known as Coulomb’s law.

Statement:
Stationary charges attract or repel each other with a force which is directly proportional to the product of magnitude of the charges and inversely proportional to the square of the distance between them.

Suppose there are two charges q₁ and q₂ which are distance r apart.
Then, according to Coulomb’s law,
\[F∝q_1q_2\]
and, \[F∝\frac{1}{r^2}\]
Combining above two equations, we get,
\[F∝\frac{q_1q_2}{r^2}\] \[\text{or, }F=k \frac{q_1q_2}{r^2}\]
where, k is proportionality constant.
The value of k depends upon;
1. The medium in which the two charges are present.
​2. The system of units in which F, q, and r are measured.

If the charges are located in air or vacuum, then,
\[k=\frac{1}{4πε_0}\]
where, ε₀ is known as permitivity of free space. Its unit is coulomb² newton⁻¹ metre⁻² (C²N⁻¹m⁻²). Its value is found to be 8.854 × 10⁻¹² C²N⁻¹m⁻².
​\[∴ F=\frac{1}{4πε_0}\cdot \frac{q_1q_2}{r^2}\]

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