Coulomb's Law and its Vector Notation

Coulomb's Law

It states that the force of attraction or repulsion between two stationary point charges in a vacuum is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them.

Mathematically, the electrostatic force between two point charges is given as

• Where, k is arbitrary proportionality constant.

• In SI units, the value of k is about 9 x 10⁹ and In CGS, the value of k is 1.

• When we put this value in the above equation

          q₁ = q₂ = 1 C, r = 1 m and k = 9 x 10⁹ 

          then, F = 9 x 10⁹ N

• Where, E₀ is called the permittivity of free space.

• In SI units, E₀ ( read as epsilon naught ) = 8.854 x 10^-12 C²N^-1m^-2.

• One Coulomb - When the charge is placed at a distance of 1 m with another charge of the same magnitude in vacuum experiences an electrostatic force of repulsion of magnitude 9 x 10⁹ N.

• In practice, we use smaller units like 1 µC or 1 mC instead of One Coulomb.

Coulomb's Law in Vector Notation

We know that force is a vector quantity, so it is better to write Coulomb's Law in vector notation. Thus, Coulomb's Force Law between two-point charge q₁ and q_{2 in vector notation is given as}