Coulomb’s Law – Conditions for Stability

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

In 1785, Charles Augustin de Coulomb, a French physicist, published the equation for the repulsive or attractive force between two electrically charged bodies, commonly known as Coulomb’s law. Coulomb’s law states that the intensity of the electrostatic force of attraction or repulsion between two electrically charged bodies is directly proportional to the product of their charges and inversely proportional to the square of their distances.

Equation of 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 metres). 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.

A point charge can be described using Coulomb’s law, which describes the force between two objects accurately. Almost as if its charge were all concentrated at its centre, the charge of a conducting sphere interacts with the charge of other objects. The centre of charge of a sphere, regardless of how uniformly the charges are distributed, can be considered its centre. A point charge resides at the centre of the sphere. Since Coulomb’s law applies to point charges, the distance between the centres of charge of each object is d in the equation.

Coulomb’s law can be expressed in the vector form as :

 F ∝  q1  q2

      F  ∝  1r2

Taking this two-equation

    F  ∝    q1q2r2

    F  =  k   q1q2r2

Coulomb’s law in scalar form is represented as: 

F = K  q1 q2 ⁄ r2

The constant of Coulomb’s law is K ⩬ 8.99 * 109N- m2 C-2, q1, q2 are the magnitudes of the charged particles, and the scalar ‘r’ is the distance between the two charged particles.

Coulomb’s law has the following properties:

A point charge tends to exert a force on another point charge to satisfy Coulomb’s law.

1. Either the attractive force or the repulsive force is involved.

2. An imaginary line will link the particles. This will be the direction of the force.

3. As the interaction includes several point charges, then each point charge deploys an individual force on each neighbouring charge, regardless of the neighbouring charges’ position.In the interaction between two charges, the force will be proportional to their magnitude.

4. Charges similar to each other tend to repel, whereas charges opposite to each other tend to attract.

5. Typically, the force between two particles or substances is inversely proportional to the square of the distance between them.

Conditions for Stability for Coulomb’s law

Suppose there are two points, A and B. If the magnitude of FA is increased when q is displaced towards A, then the magnitude of FB decreases.

Consequently, it will not return to its original position since all the force on q is directed towards A. Consequently, an axial displacement will cause the equilibrium to break down.

The charge is returned to its original position when “q” is perpendicular to AB because the forces FA and FB oppose each other. As a result, the equilibrium is stable in the case of a perpendicular displacement.

1 Coulomb of Charge is defined as a charge that repels another charge of the same sign with a force equal to 9*10 N while the charges are separated by one metre in a vacuum, and the Coulomb force is defined as the conservative internal force.

Its value is 8.86 × 10-12 C²/N m2 = 8.86 × 10-12 F m-1 

This tells us how the Coulomb force will be true only for the static charges.

Limitations of Coulomb’s law

Coulomb’s law is derived under definite assumptions and cannot be applied liberally. Its limitations are as follows:

• If the average number of solvent molecules between two interesting charge particles is large, Coulomb’s law holds.

• The point charges must be at rest for Coulomb’s law to apply.

• Coulomb’s law is invalid if charged bodies are of limited dimension such that they can’t be considered a point charge. Thus, Coulomb’s law does not apply to distances below 10-15 cm.

• The inverse-square law applies to Coulomb’s law. It is only appropriate in cases where the inverse square law applies.

• Solvent molecules between particles must be larger than both charges to be valid.

• Charges with regular and smooth shapes can be handled easily with this formula, but charges with irregular shapes become too complicated.

Conclusion

Coulomb’s law states that the force of attraction between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between the two. The charge acts along the line that connects the two points. 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.