Question

Which of the following represent Coulomb’s constant?
$\text{A}\text{. }k=\dfrac{1}{4\pi {{\varepsilon }_{0}}}$
$\text{B}\text{. }k=1+4\pi {{\varepsilon }_{0}}$
$\text{C}\text{. }k=1-4\pi {{\varepsilon }_{0}}$
$\text{D}\text{. }k=1\times 4\pi {{\varepsilon }_{0}}$

Answer 1

The magnitude of electrostatic force between two point sized charged particles (say ${{q}_{1}}$ and ${{q}_{2}}$) at rest and separated by a distance r is given as $F=\dfrac{k{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}$. It is also given as $F=\dfrac{{{q}_{1}}{{q}_{2}}}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}$. From these equations find the relation between k and ${{\varepsilon }_{0}}$.

Complete step by step answer:
Let us first understand what Coulomb's law is.
Coulomb’s law is the law, which tells us about the electrostatic force between two charged particles, both at rest. According to Coulomb's law, every charged particle exerts a force on another charged particle. This force is called an electrostatic force or Coulomb force if the charged particles are at rest.

The magnitude of electrostatic force between two point sized charged particles (say ${{q}_{1}}$ and ${{q}_{2}}$) at rest and separated by a distance r is given as $F=\dfrac{k{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}$. Here, k is a proportionality constant called Coulomb’s constant.

It is found that the value of the Coulomb force changes with change of the medium surrounding the two charges. Therefore, the electrostatic force between two charged particles depends on the medium in which the particles are placed. Hence, we define a quantity for a medium called electrical permittivity of the medium ($\varepsilon$).
If the medium is vacuum then its electrical permittivity is denoted as ${{\varepsilon }_{0}}$.

Thus it is found that $k=\dfrac{1}{4\pi {{\varepsilon }_{0}}}$. Hence, the correct option is A.

Note: If you get confused in understanding the concept of electrostatic force between two charged particles, then you can correspond it to the concept of gravitational force between two masses. The electrostatic force between two charged particles is similar to the gravitational force between two masses. The magnitude of gravitational force between two point sized particles of masses ${{m}_{1}}$ and ${{m}_{2}}$ that are separated by a distance r is given as $F=\dfrac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}$.
Here, G is a proportionality constant called gravitational constant.