# Coulomb’s Law

Coulomb’s Law :-

On the basis of experiments, Coulomb established the following law known as Coulomb’s law.

The magnitude of electrostatic force between two point charges is (i) directly proportional to the product of charges and (ii) inversely proportional to the square of the distance between them.

i.e.  $\displaystyle F\propto {{q}_{1}}{{q}_{2}}$

and $\displaystyle F\propto \frac{1}{{{r}^{2}}}$

$\displaystyle F\propto \frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}$

or

$\displaystyle F=k\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}$

Important points regarding Coulomb’s law :

(a) It is applicable only for point charges.

(b) The constant of proportionality K in SI units in vacuum is expressed as 1/4πε0 and in any other medium expressed as 1/4πε . If charges are dipped in a medium then electrostatic force on one charge is $\displaystyle F=\frac{1}{4\pi {{\varepsilon }_{0}}{{\varepsilon }_{r}}}\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}$ .  ε0 and ε called permittivity of vacuum and absolute permittivity of the medium respectively. The ratio ε/ε0 = εr is called relative permittivity of the medium, which is a dimensionless quantity.

(c) The force acting on one point charge due to the other point charge is always along the line joining these two charges. It is equal in magnitude and opposite in direction on two charges, irrespective of the medium, in which they lie.

(d) Since the force is a central force, in the absence of any other external force, angular momentum of one particle w.r.t. the other particle (in two particle system) is conserved.

(e) The value of relative permittivity εr is constant for medium and can have values between 1 to ∞. For vacuum, by definition it is equal to 1. For air it is nearly equal to 1 and may be taken to be equal to 1 for calculations. For metals the value of εr is ∞ and for water is 81. The material in which more charge can induce εr will be higher.

(f) The value of 1/4πε= 9 × 109 Nm2 C–2    ⇒   ε0 = 8.855 × 10–12 C2/Nm2.
Dimensional formula of e is [M–1 L–3 T4 A2]

(g) The force is conservative in nature i.e., work done by electrostatic force in moving a point charge along a close loop of any shape is zero.

Here is a video lecture on Coulomb’s Law in which Coulomb’s Law is explained in details that how Coulomb deduced this law using Torsion Balance:-

Video particularly on Torsion Balance used in Coulomb’s Law:-

Video lecture on Coulomb’s Law:-