Value of k in Electrostatics: Coulomb’s Constant Explained

The value of k in electrostatics is worth learning while diving into Coulomb's Law for exams. We uncover the mathematical relationship with how charges separated by a distance interact in any medium using this very value of k in physics. 

When learning the Coulomb’s Law formula, we should have one thing in the back of our heads, ie., the value of k in electrostatics.  It is 8.9875 x 10^9 N m^2 /C ^2. This k value in physics has many other names. Electrostatic constant. More preferably, for exams, it’s called Coulomb’s Constant.
If you want to dig deep into why this exact value exists, in what type of medium will it be constant, or simply need to tackle those tricky Class 12 Physics Chapter 1 Solutions, read about this here today. 

What is k Value in Physics? 

k or Coulomb’s constant, is a proportionality constant in the formula for electrostatic force F = k x q_1q_2 /r^2.  We can find in some sources to be denoted as k_e or with a capital K. 

This k value in a complete vacuum is k = 8.9875×10^9 N m^2 /C ^2. Sometimes it's rounded off to k = 9×10^9 N m^2 /C ^2. 

We use the medium's permittivity to determine k, which is the property that tells us how much of the electric field gets reduced in the medium when two charges are there, and which is shown in the general equation when the medium is vacuum, as k = 1/4πε_0. Here, ε_0 means it’s a vacuum. 

Coulomb’s Law cannot be defined without this k value, as it converts the proportionality in the equation, where:

• Force is directly in proportion to the product of the two charges F ∝ q_1q_2 

• Also, this same force has an inverse proportionality to the distance, squared between the two charges, ie., F ∝ 1/ r^2.  

Factors that Affect the Value of k in Electrostatics

We need to know two factors directly affecting the Coulomb constant or k value in physics.
One is the nature of the medium. We will see below how vacuum has the highest value of k as compared to other media.

Second is the system of units we use. While we go by SI units standards, in some competitive exams you may be asked to define it by CGS standards. 

How the International System of Units Describes the Value of k in Electrostatics

As you go back to units and measurement Class 11 notes, remember you must use the SI unit that is universally accepted. This Coulomb constant or k, which is the strength of the electrostatic force, is an expression of the free space permittivity ε_0 using k=1/4πε_0. 

In the SI unit standards there are two k values you can remember

1. Standard Approximate Value: The value of k = 9×10^9 N m^2 /C ^2 is the closest one and the medium is air. 
2. Precise Value: Just in case you need to remember, there is a precise one that’s recommended by CODATA 2022, based on which, we must use the value of k as 8.9875 x 10^9 N m^2 /C^2. 

What to use as the SI unit of k? Simple, Newton metre squared per Coulomb squared. 

If we look at the equation of F = k q_1q_2/r^2, we simply rearrange the order just to get k, which would look like 

k = Fr^2/q_1q_2

Now let’s substitute SI Units for each quantity, where Force, F is Newtons, distance, r is metre, and charges, q_1 and q_2 and their product would be Coulomb. 

So the units of k or the final SI Unit of Coulomb’s Constant or k become 

[k] = Nm^2/C^2

Think what this SI unit is telling us.

When every Coulomb of charge gets squared and when the two charges have a separation of one metre and that's squared, the electrostatic force has a magnitude of k Newtons. 

k value in Physics in Other Systems

When we look at the CGS system, the common unit of charge is the statcoulomb (statC) or the Gaussian form, esu. The Coulomb Constant here does not have any dimension, and k value is considered as 1. The equation in the CGS unit when using the Coulomb’s Law formula just becomes F = q_1q_2/r^2. 

How Does Medium Affect the Value of k in Electrostatics?

The epsilon symbol ε that we used earlier mathematically defines the absolute permittivity of the medium that surrounds the charges. 

We use the naught, ε_0, only to define that the medium is vacuum or air between the charges. And mind you, the electrostatic force here is at its maximum.

Because in other surroundings or media apart from air, the force between the charges would drastically decrease as there would be some resistance to the electric field.

That’s where we’d be using relative permittivity, which is also known as the dielectric constant and ε_r it is denoted as. 

A dielectric medium is like an insulator, resisting electricity from passing through. In the same manner, this dielectric constant or that we call relative permittivity shows us how much the medium really reduces the electric field when comparing it to the vacuum.  

We can mathematically now use this expression for absolute permittivity.

ε = ε_0 ε_r

So if we have to measure the value of k in any medium, we’ll use 

k_medium =  1/4πε = 1/4πε_0 ε_r = k_vacuum/ε_r

So, if this relative permittivity, ε_r increases, k_medium is going to decrease and the force will weaken.  

Importance of k Value in Physics Class 12

Looking at k from the maths angle, we can say that k is a highly precise factor. It converts the relationship in experiments, such as finding the proportionality of force, electric charges, and the distance, and gives us an equation that’s universally consistent with SI units. 

k is also a physical quantity. Part of it is why we learn this in the electric charge class 12 chapter. It can easily tell us how any medium like air or water allows an electric field to interact between charges. When k has a higher value, there will be more electrostatic force for an amount of charge and separation.
And if you really have to see how k defines the direction and magnitude of this electrostatic force, you should read up on the vector form of Coulomb’s Law. 

Approaching Exams with the Value of k in Electrostatic Force

You can ideally prepare for competitive exams by focusing on a few things about the k value. 

One is where you may have to compare the value of k in electrostatic forces vs gravitational forces like finding the force ratio between protons and electrons.

Second, which is easier, finding force between two charges in different media where you have to remember using the concepts of absolute and relative permittivity.