Coulomb's Law - Vector form 1

Description:

We know that force in q vector quantity, so it will have magnitude as well as directon.

F = 1/4πε_o q₁q₂/r²

This equation gives only magnitude.

Notation for direction

• Consider the direction q₁ to q₂

• ‘r’ is the displacement between them. So, displacement in the vector form can be written as −

  (r₂₁→ denotes, displacement upto point 2 from point 1)

  Now, Vector r₂₁→ can be written as −

r₂₁→ = r̂₂₁ |r₂₁|→

Here −

‘r₂₁’ is a full vector

‘r̂₂₁’ is a unit vector

|r₂₁|→ is the magnitude

Coulumb Force Vector

Coulumb Force is always along the straight line going the two charges.

Let,

• Both the charges are similar.

• Q2 is experiencing force due to q₁. So, force vector can be written as −

  F₂₁→

F₂₁→ represents, force on charge q₂ due to charge q₁.

So, Vector equation of coulomb force can be written as −

Format 1 − F₂₁→ = 1/4πε_o q₁q₂/r² r̂₂₁ .....(1)

(Unit vector r̂₂₁, its magnitude is always equal to 1. So, it doesn’t charges value, it only gives the direction)

We know that r̂₂₁ = r₂₁→/r .....(2)

Putting (2) in (1) we get −

Format 2 − F₂₁→ = 1/4πε_o q₁q₂/r³r₂₁→