Question

Derive an expression for Coloumb's Law​

Answer 1

Coulomb's law states that: The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.

Derivation In Attachment

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Answer 2

$\huge\mathfrak{\red{COLOUMB'S\:\:LAW}}$

It states that the force of attraction or repulsion between two charged bodies is directly proportional to the product of charges in the two bodies and inversely proportional to the square of distance between them.

Mathematically,

$F\propto q_{1}q_{2}$. ........... (1)

$F \propto \dfrac{1}{r^{2}}$ ........... (2)

where

• $q_{1}\:and\;q_{2}$ are two charges.
• r is the distance of separation.
• F is the Force.

______________________________________

On combining equations (1) & (2) we have,

$\implies F\:\: \propto\:\:\dfrac{q_{1}q_{2}}{r^{2}}$

$\implies F \:\: =\:\: k\dfrac{q_{1}q_{2}}{r^{2}}$

$\implies F \:\:=\:\:\dfrac{1}{4\pi\epsilon_{0}}\dfrac{q_{1}q_{2}}{r^{2}}$

$\large\red{\underline{\boxed{\purple{F \:\:=\:\:\dfrac{1}{4\pi\epsilon_{0}}\dfrac{q_{1}q_{2}}{r^{2}}}}}}$