Question

State Coulomb’s law in electrostatics and represent it in vector form.

Answer 1

Coulombs law :- Definition
According to the Coulomb law, the Magnitude of the Force of Repulsion of the charges Or magnitude of the Force of attraction is directly proportional to their products of the magnitude of these charges and inversely proportional to the square of distance between these charges. 
Numerically, It can be written as ⇒
F ∝ q₁q₂/r²where q₁ and q₂ are the magnitude of the charges. and r is the distance between them.
∴ F = kq₁q₂/r²

k is the Coulomb law constant.Its value is 8.99 × 10⁹ Nm² C⁻². It is commonly written as 9 × 10⁹ Nm² C⁻².
In Vector Form :-  It can be written as solved in the given attachment.



Hope it Helps.

Answer 2

Coulomb’s law in electrostatics :

 " The magnitude of the force between any two point charges is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square  of distance between them and the force always acted along the line joining the two charges."

If two point charges q1 qnd q2 are separated by a distance r in vacuum and F is the magnitude of fore between them, according to Coulomb's law:

F α (q1 q2 )/ r2

F=K (q1 q2 )/r2

where K is constant. The value of k depends upon nature of medium.
Usually in vacuum , K=1/4πε₀

So coulomb's law can be written as : F= (1/4 πε₀  ) (q1 q2)/r2

Coulomb's law in Vector form :

Let the positions of vectors of charges q1 and q2 be r1 and r2 .
we denote force on q1 due to q2 by F12 and force on q2 due to q1 by F21.

F21=k (q1 q2)/r²₂₁ (r₂₁)


F12=k (q1 q2)/r²12 (r₁₂)

F12=-F21

Please refer the attachment for vector form