magnetic flux density — from formula anatomyMagnetic flux density, often denoted as B, is a vector field that describes the strength and direction of a magnetic field at every point in space. It is the fundamental quantity that determines the force a moving charge experiences (via the Lorentz force) and the torque on a magnetic dipole. In everyday terms, it tells you how 'strong' a magnet is and in which direction it pushes on charged particles. The SI unit is the tesla (T), where 1 T = 1 kg/(A·s²).
The concept evolved from Michael Faraday's lines of force in the 1830s. James Clerk Maxwell formalized it mathematically in his 1865 paper 'A Dynamical Theory of the Electromagnetic Field', and the modern vector calculus formulation was completed by Oliver Heaviside and Josiah Willard Gibbs in the 1880s.
Magnetic flux density arises from moving electric charges (currents) and from intrinsic magnetic moments of particles. It is defined through the Lorentz force law: F = q(v × B), where F is force, q is charge, and v is velocity. The 'flux density' name comes from the concept of magnetic flux Φ, which is the integral of B over a surface: Φ = ∫ B · dA. Thus, B is the flux per unit area. In materials, B is related to the magnetic field strength H by B = μ₀(H + M), where μ₀ is the vacuum permeability and M is the magnetization.
Magnetic flux density is central to the design of electric motors, generators, transformers, MRI machines, and particle accelerators like the LHC, where superconducting magnets produce fields up to 8 T.
The strongest magnetic fields in the universe are found on neutron stars called magnetars, with flux densities up to 10¹¹ T — about a trillion times stronger than a typical refrigerator magnet.
| E | variable | Energy of the charged particle — energy joule |
| B | variable | Magnetic field strength — magnetic flux density tesla |
| m | variable | Mass of the charged particle — mass kilogram |
| \hbar | constant | Reduced Planck constant, quantum of angular momentum — reduced planck constant = 1.054571817e-34 joule second |
| e | constant | Magnitude of electric charge of a proton or electron — elementary charge = 1.602176634e-19 coulomb |
| c | constant | Speed of light in vacuum, universal constant — speed of light = 299792458 metre per second |
| n_e | variable | electron number density — electron number density per cubic metre |
| B_parallel | variable | magnetic field component along line of sight — magnetic flux density tesla |
| dl | variable | infinitesimal path element along line of sight metre |
| e | constant | elementary charge — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | electron rest mass — electron mass = 9.1093837015e-31 kilogram |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | summation over the line of sight — integral operator |
| \nu_c | variable | Critical synchrotron frequency — frequency hertz |
| \gamma | variable | Lorentz factor of electron — lorentz factor |
| e | variable | Elementary charge — elementary charge coulomb |
| B | variable | Magnetic field strength — magnetic flux density tesla |
| m_e | variable | Electron rest mass — electron mass kilogram |
| c | variable | Speed of light in vacuum — speed of light metre per second |
| l_B | variable | Magnetic length — length metre |
| B | variable | Magnetic field strength — magnetic flux density tesla |
| ħ | constant | Reduced Planck constant, fundamental quantum of angular momentum — reduced planck constant = 1.054571817e-34 joule second |
| e | constant | Elementary charge, the magnitude of charge of an electron — elementary charge = 1.602176634e-19 coulomb |
| √ | operator | Square root of the argument — square root |
| t | variable | Spin-down timescale — time second |
| P | variable | Rotation period — time second |
| B | variable | Magnetic field strength at the surface — magnetic flux density tesla |
| ν_c | variable | Cyclotron frequency — frequency hertz |
| e | variable | Elementary charge — elementary charge coulomb |
| B | variable | Magnetic field strength — magnetic flux density tesla |
| m_e | variable | Electron mass — electron mass kilogram |
