LIMITATIONS OF COULOMB'S LAW:

1)Applicable only in cases when inverse law works.

2)Applicable For Point Charges at Rest.

3)It is Difficult to apply Coulomb's Law,when charges are in arbitrary shape.

The Limitations of Coulomb's Law

Coulomb's law is a fundamental principle in electrostatics that describes the force between two charged particles. It states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. While Coulomb's law is a useful tool for calculating electrostatic forces in many situations, it does have some limitations.

1. Point Charges
Coulomb's law assumes that the charges involved are point charges, which means that their sizes are negligible compared to the distance between them. In reality, most charged objects have a finite size, and the distribution of charge within an object can affect the force it experiences. Coulomb's law does not take into account the effects of the size or shape of the charged objects.

2. Continuous Charge Distribution
Coulomb's law is applicable to point charges or charged objects with a discrete distribution of charge. However, in many situations, charged objects have a continuous distribution of charge, such as a charged wire or a charged sphere. Coulomb's law cannot be directly applied to such cases, and more advanced mathematical techniques, such as integration, are required to calculate the force.

3. Relativistic Effects
Coulomb's law is based on classical electrodynamics, which assumes that the charges are stationary or moving at speeds much lower than the speed of light. At high speeds or in situations involving strong electromagnetic fields, relativistic effects become significant, and Coulomb's law is no longer accurate. In such cases, the more comprehensive theory of electromagnetism, described by Maxwell's equations, must be used.

4. Quantum Effects
At the atomic and subatomic level, the behavior of charged particles is governed by quantum mechanics. Coulomb's law does not account for quantum effects, such as the wave-particle duality of electrons or the uncertainty principle. In these situations, quantum electrodynamics, which combines quantum mechanics and electromagnetism, is required to accurately describe the behavior of charged particles.

5. Non-electrostatic Forces
Coulomb's law only describes the electrostatic forces between charged particles. It does not account for other types of forces, such as magnetic forces or gravitational forces, which may also be present in certain situations. To fully understand the forces acting on a system, one must consider all relevant forces, including those beyond the scope of Coulomb's law.

In conclusion, while Coulomb's law is a useful tool for calculating electrostatic forces in many situations, it has limitations when applied to charged objects with finite size, continuous charge distributions, relativistic speeds, quantum effects, and non-electrostatic forces. To accurately describe and analyze such situations, more advanced theories and mathematical techniques are necessary.