Key Points on Coulomb’s Law

Coulomb’s Law describes the force that exists between two stationary, electrically charged particles, also known as electrostatic force. 

Coulomb’s Law acts along the line connecting the two charged bodie’s centres. The law is also known as Coulomb’s inverse-square law because it describes an inverse square relationship between force and distance between two charged entities. Coulomb’s Law is regarded as an electrical equivalent of Newton’s Universal Law of Gravitation since the relation it derives is quite similar to the gravitational force acting between two large masses.

What is Coulomb’s Law?

According to Coulomb’s Law, the energy between two charged objects is proportional to their respective charges and inversely proportional to their separation distance. This can be expressed mathematically as:

F= k * Q1* Q2/ d2

Object 1 is charged with Q1 (in Coulombs), object 2 is charged with Q2, and d is the distance between the two objects (in meters). The letter K represents Coulomb’s Law constant k. 

The value of k depends upon the medium in which the charged objects are immersed. As for air, the value is approximately 9.0 x 109 N /m2 /c2. In the equation, k is substituted for Coulombs, removing the units of distance and charge. This leaves Newtons as the unit of force

Important aspects of Coulomb’s Law

• In accordance with Coulomb’s Law, the electrostatic force is directly proportional to the product of the magnitude of the two point charges and inversely proportional to the square root of the distance between them.
• The SI unit is k = 1/4₀ and its value is 9 × 109 N m2/ C2. ∈0 denotes the permittivity of free space or vacuum and the value of ∈0 is 8.85 × 10-12 C2N-1m-2.
• The charge q1 always exerts a force on the charge q2 along the line connecting the two charges. r12 is the unit vector pointing from charge q1 to q2. And the force on the charge q1 exerted by q2 is along – r12.
• In SI units, Coulomb’s Law in a vacuum takes the form F21=1/4₀.q1.q2/ r2 r21ˆ .In a medium permittivity ∈, the force between two point charges is given by  F21=1/4.q1.q2/ r2 r21ˆ.

The relative permittivity for a given medium as ∈r = /₀. For a vacuum or air  ∈r = 1, and for all other media ∈r > 1.

• The force between two point charges in a medium other than a vacuum is always less than the force in a vacuum since, ∈ > ∈0.
• When two charges of one Coulomb are separated by a distance of 1 m, the electrostatic force between them is calculated as follows:

|F| = 9×109×1×1 / 12= 9 × 109N

• This is a huge quantity, almost equivalent to the weight of one million tons. We never come across 1 Coulomb charge in practice. Electrical charges on a daily basis can be measured in micro Coulombs or nano Coulombs.
• Newton’s law of gravitation has the same structure as Coulomb’s Law. The two are inversely proportional to the square of the distance between the particles. Two points of charge produce an electrostatic force directly proportional to their magnitude, and two masses produce a gravitational force directly proportional to their magnitude. However, these laws differ in several important ways.
• A gravitational force between two masses is always attractive, while a Coulomb force between two charges may be either attractive or repellent, based on how the charges are arranged.
• The value of the gravitational constant G = 6.67 × 10-11 Nm2kg-2. The value of the constant k in Coulomb law is k = 9 × 109  Nm2C-2. Since k is much greater than G, the electrostatic force is always greater in magnitude than the gravitational force for smaller size objects.
• Two masses are attracted by their gravitational force regardless of the medium in which they are located. The gravitational force between two masses remains the same if 1 kg of each mass is kept in air or water. In fact, the electrostatic force between two charges depends on the medium in which they are held at rest.
• An electric charge q1 is exerted by a point charge q2.

 F12→=1/4₀.Q1.Q2/ r2 r12ˆ

Since, r21= r2 – r1

F12→=1/4₀.Q1.Q2/ r2 ( -r21ˆ)

= – 1/4₀.Q1.Q2/ r2 r21ˆ

                                  F12= – F21

As a result, electrostatic forces obey Newton’s third law.

• It is only true for point charges that Coulomb force can be expressed. However, point charges are idealised. Nevertheless, Coulomb’s Law can be applied to two charged objects whose sizes are very much smaller than the distance between them. The first Coulomb law was discovered as a result of looking at charged spheres of the torsion balance as point charges. Two charged spheres are separated by a distance that is much greater than their radius.

Conclusion

The electric force is inversely proportional to the square of Coulomb’s Law. Furthermore, this law is used in deriving Gauss’ law accurately for general cases. Charges at rest exert the following properties according to Coulomb’s Law- where like charges repel one another and unlike charges attract each other. The vector form of Coulomb’s Law provides the direction of electric fields caused by charges. Two negative charges repel one another, while a positive charge attracts a negative charge. In physics, charges act in accordance with their lines of attraction.