Coulombs Law: Coulombs law is a fundamental law of physics that describes the interaction between electric charges. It states that the force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them.

Coulombs Law Formula

Mathematically, Coulombs law can be expressed as:

F = k x (q₁ x q₂) / r²

where F is the force between the charges, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the Coulomb constant, which has a value of approximately 8.99 x 10⁹ N m²/C².

Formula

F ∝ q₁q₂/d²

where,

• ε is absolute permittivity,
• K or ε_r is the relative permittivity or specific inductive capacity 
• ε₀ is the permittivity of free space.
• K or ε_r is also called a dielectric constant of the medium in which the two charges are placed.

Properties of the Coulombs Law

Coulombs law is a fundamental law of electrostatics that describes the interaction between electrically 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. The following are the key properties of Coulomb’s law:

• Direction of force: The force between two charges is always along the line connecting the two charges. If the charges are of the same sign (either both positive or both negative), the force between them is repulsive. If the charges are of opposite sign, the force between them is attractive.
• Proportional to charge: The force between two charges is directly proportional to the magnitude of each charge. The larger the charges, the greater the force between them.
• Inversely proportional to distance: The force between two charges decreases as the distance between the charges increases. This is because the force is spread over a larger area, reducing the intensity of the force.
• Vector quantity: The force between two charges is a vector quantity and has both magnitude and direction. The direction of the force is determined by the direction of the line connecting the two charges, as described above.
• Additive forces: The force between multiple charges can be determined by considering the forces between each pair of charges and then adding these forces vectorially.
• Distance dependence: Coulomb’s law applies only for point charges and only for the case of infinite distances. For charges with finite size and for charges in close proximity, other electromagnetic effects come into play and Coulomb’s law may not hold.

Limitations of Coulombs Law

Coulombs law is a widely used and powerful law of electrostatics, but it does have some limitations:

• Point charges: Coulomb’s law applies only to point charges, meaning that the charges have zero size and are located at a single point in space. In reality, charges have finite size and distribution, and Coulomb’s law is only an approximation for real-world charges.
• Infinite distances: Coulomb’s law applies only to charges that are far apart, meaning at infinite distances. When charges are brought close together, other electromagnetic effects come into play and Coulomb’s law may not hold.
• Inapplicability to conductors: Coulomb’s law is not applicable to conductors, meaning that the charges are free to move within the conductor and are not confined to a specific location. In this case, other electromagnetic effects, such as the electric field within the conductor, must be taken into account.
• Inapplicability to moving charges: Coulomb’s law applies only to stationary charges. When charges are in motion, other electromagnetic effects, such as the magnetic field generated by the moving charges, must be taken into account.
• Relativity: Coulomb’s law is based on classical electromagnetism and does not take into account the effects of special or general relativity. For charges moving at relativistic speeds or for charges near massive objects, the electromagnetic interactions may be different from those predicted by Coulomb’s law.

Applications of Coulombs Law

Coulombs law has numerous applications in physics and engineering, some of which are:

• Electrostatic charging: Coulomb’s law is used to explain the behavior of charged objects, including the ways in which they can become charged (such as by friction or induction), and how they interact with other charged objects.
• Electric fields: Coulomb’s law is used to calculate the electric field generated by a charged object, and the force experienced by other charged objects in the field.
• Electrostatic separation: Coulomb’s law is used in the design of equipment for separating different materials based on their electric charge. For example, it is used in the separation of minerals in the mining industry.
• Electrophoresis: Coulomb’s law is used to explain the behavior of charged particles in electrophoresis, a technique for separating charged particles in a solution.
• Capacitance: Coulomb’s law is used to calculate the capacitance of a capacitor, which is a device used to store electric charge.
• Ion thrusters: Coulomb’s law is used in the design of ion thrusters, which are electric propulsion systems used in spacecraft to generate thrust.
• Electrometers: Coulomb’s law is used to calibrate electrometers, which are instruments used to measure electric charge.

• Charged particle beams: Coulomb’s law is used to understand the behavior of charged particle beams in accelerator and collider experiments, where beams of charged particles are accelerated to high speeds and then made to collide with other particles.

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By Team Learning Mantras