Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Electromagnetism → Electrostatics ↓


Coulomb's law


Coulomb's law is a fundamental principle in electrostatics, a branch of electromagnetism. This law describes the force between two stationary charged particles. It is essential to understanding the behavior of electric charges in the universe. Named after French physicist Charles-Augustin de Coulomb, who first published this law in 1785, this law plays a similar role to Newton's law of universal gravitation, but in electrical terms.

What is Coulomb's law?

Coulomb's law states that the magnitude of the electrostatic force of interaction between two point charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The force is also directed along the line joining the two charges.

F = k * |q1 * q2| / r²

Where:

  • F is the magnitude of the force between the charges.
  • k is the Coulomb constant, approximately 8.9875 × 10⁹ N m²/C².
  • q1 and q2 are the amounts of fees.
  • r is the distance between the centres of the two charges.

Understanding the formula

The formula expresses that the force increases with the increase in charge values and decreases with the square of the distance between them. This inverse square relationship is common in physics, as seen in the force of gravity.

Direction of force

Coulomb's law tells not only the magnitude of the force but also the direction. If the charges are both positive or both negative, they repel each other. If one charge is positive and the other is negative, they attract each other.

Visual example

Consider two charged particles Q1 and Q2 separated by a distance r:

Q1 Q2 R

If the charges of Q1 and Q2 are equal, then the forces acting on each charge are directed away from each other. If their charges are opposite, then the forces are directed towards each other.

A real-world example

Suppose you have two spherical balloons rubbed on a sweater. Each balloon becomes charged due to the transfer of electrons when they contact the sweater and each other. Imagine the balloons as having charges Q1 and Q2. If they are brought close to each other, you will notice a force between them, which is a manifestation of Coulomb's law.

Unit of charge

The standard unit of charge is the coulomb (C). One coulomb is approximately equal to the charge of 6.242 × 10¹⁸ electrons. Charge is quantized, which means it exists in discrete packets, and the charge of electrons is one such packet.

Importance of Coulomb constant

The constant k, known as the Coulomb constant, represents the electrostatic force between two point charges in a free space vacuum. Its value can vary depending on the medium where the charges are located. For example, water and glass have dielectric properties that can reduce the effective value of k.

Vector nature of electrostatic force

Coulomb's law is often expressed in vector form to indicate the direction and magnitude of the force. Vector form can be particularly useful when calculating forces in three-dimensional spaces.

F = k * q1 * q2 * (r / r³)

Where F represents the force vector, and r is the vector separating the two charges. Division by r³ ensures that the careful directional component is considered along with the distance.

Superposition principle

When multiple charges are present, the total electrostatic force on a particular charge is the vector sum of the forces exerted by all the other charges. This additive property is known as the superposition principle.

Example with multiple charges

Imagine that three charged particles Q1, Q2, and Q3 are present in one space:

Q1 Q2 Q3

The forces on Q1 due to Q2 (F 12) and Q3 (F 13) must be added vectorially to find the net force on Q1.

F 1 = F 12 + F 13

Limitations of Coulomb's law

Coulomb's law assumes point charges, which means that it is most accurate when the sizes of the charged bodies are negligible compared to the distance between them. If this condition is not met, more advanced methods involving field theory may be needed. The law also does not apply accurately to moving charges, where magnetic effects become important.

Historical context

Investigations into the nature of electrical forces were carried out before Coulomb's law and involved many other luminaries such as Benjamin Franklin and Michael Faraday. Coulomb's work helped formalize and quantify earlier experimental observations into a coherent mathematical framework.

Importance in modern physics

Coulomb's law underlies much of modern electrical theory, serving as a cornerstone for the development of electric potential, electric fields, and much more. It is important in the fields of chemistry and atomic physics, where it describes the forces in the electron configuration around atoms.

Combining classical and quantum approaches

In quantum mechanics, forces are often calculated in terms of fields and their potentials, but the principles of Coulomb's law persist in explaining forces on the atomic scale. For example, the interactions between electrons in atomic orbitals and protons in the nucleus can be analyzed using the quantum mechanical form of Coulomb's law.

Summary

Coulomb's law is a simple but comprehensive framework that governs the electrostatic interactions between charged particles. Its mathematical form has universal applicability at all scales, from subatomic particles to macroscopic objects. Its principles laid the foundation for much of today's classical and modern physics.


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Coulomb's law

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