# Coulomb’s law and its limitations

In this article, we will discuss how Coulomb’s law explains that two charges placed at a certain distance apart interact with each other.

**COULOMB’S LAW**

**Statement.** The force of interaction between two stationary point charges q1 and q2 is directly proportional to the product of the charges and inversely proportional to the square of the distance r between them.

That is,

F α q1q2/r^{2}

If the charges are placed in a vacuum, then

F = 1/4Пε_{o} q1q2/r^{2}

where 1/4Пε_{o} is a proportionality constant.

ε_{o} is the permittivity of free space = 8.85418 x 10^{-12 }C^{2} /Nm^{2} or Farad/m

In the below diagram, **F**_{12} is the force exerted by charge *q*1 on charge *q*2 and *a** _{r} *is the unit vector. The force exerted by charge

*q*2 on charge

*q*1 is

**F**

_{21}. Thus,

**F**

_{21}= –

**F**

_{12}

**Definition of coulomb:** One coulomb is defined as the quantity of charge, which when placed 1 meter from an equal and opposite charge in a vacuum, repels it with a force of 9.0 x 10^{9} N.

**Limitation Of Coulomb’s Law:**

It is difficult to apply the law when charges are of arbitrary shape. Here, the distance, r cannot be determined accurately as the centres of arbitrarily shaped charged bodies cannot be identified accurately.

This is all about Columb’s law statement or meaning, derivations, and limitations of Coulomb’s law. From Coulomb’s law, we can discuss Electric Field Intensity then Gauss’s Law that I have discussed in separate articles. The following is our Youtube video on Coulomb’s law, its derivation and limitation:

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thanks