# Formulas with c

Introduction

The speed of light, denoted as “c,” stands as a fundamental constant in physics, shaping various theories and equations. Its value, 299,792,458 meters per second in a vacuum, serves as a cornerstone for understanding the relationship between energy, matter, and spacetime. The following formulas underscore the critical role of c in modern physics:

Note: In addition to the direct implication of the speed of light (c) in various formulas, it’s worth noting that the fundamental unit of length in the International System of Units (SI), meters (m), is also indirectly tied to the speed of light. The definition of the meter is derived from the distance traveled by light in a vacuum in a specific fraction of a second. Therefore, any formulas involving meters implicitly incorporate the speed of light as a fundamental constant.

Einstein’s Mass-Energy Equivalence: E=mc²

This equation, famously known as Einstein’s mass-energy equivalence, demonstrates the interconversion of mass and energy. It reveals that energy (E) is directly proportional to mass (m) and is equal to the mass times the speed of light squared.

Relativistic Kinetic Energy: K=(γ−1)mc²

The relativistic kinetic energy formula accounts for the increase in kinetic energy as an object approaches the speed of light. It incorporates the Lorentz factor (γ) to adjust for relativistic effects.

Lorentz Factor: γ=1/√(1−v²/c²)

The Lorentz factor is pivotal in relativistic physics, describing how time, length, and relativistic mass change for an object moving relative to an observer. It quantifies the dilation of time and contraction of length as velocity approaches the speed of light.

Permeability of Free Space (μ₀)

The permeability of free space characterizes how magnetic fields propagate through a vacuum. Its value, influenced by the speed of light, impacts the behavior of electromagnetic waves and phenomena.

Permittivity of Free Space (ε₀)

The permittivity of free space dictates the ability of a vacuum to permit the displacement of electric field lines. It plays a crucial role in determining the strength of electric fields and the behavior of charged particles.

Fine-Structure Constant (α) α=e2 / 4πε0ℏc

The fine-structure constant represents the strength of the electromagnetic interaction between elementary charged particles. Its value, dependent on the speed of light, influences the fine structure of atomic spectra and fundamental forces.

Planck’s Constant (h)

Planck’s constant is a fundamental constant in quantum mechanics, relating the energy of a photon to its frequency. It forms the basis of quantum theory and governs the quantization of energy at the microscopic level.

Electron volt (eV/c²)

The electron volt divided by the speed of light squared represents a unit of energy commonly used in atomic and particle physics. It provides a convenient scale for describing the energy of subatomic particles.

Maxwell’s Equations

Maxwell’s equations describe the behavior of electric and magnetic fields, laying the foundation for classical electromagnetism. These equations, incorporating the speed of light, unify electricity, magnetism, and light phenomena into a cohesive framework.