Magnetic Field: Flux Density, Permeability & Lorentz Force Equations
Authoritative guide to magnetic flux density (B), magnetizing intensity (H), Maxwell's equations, and SI unit conversions across MRI and industrial electromagnetics.
Lorentz Force & Magnetic Flux Density (B)
Magnetic flux density B is defined through the magnetic component of the Lorentz Force Law acting on a moving charged particle:
Lorentz Force Equation (F = Force in Newtons, q = Charge, v = Velocity, B = Magnetic Flux Density in Tesla)
One Tesla represents the magnetic flux density that exerts a force of 1 Newton on a charge of 1 Coulomb moving perpendicular to the magnetic field at a velocity of 1 meter per second.
SI Tesla vs. CGS Gauss & Oersted Standards
Magnetics engineering historically developed under the Gaussian CGS system:
SI Standard: Tesla (T) & A/m
1 Tesla equals 1 Weber / m² = 1 N / (A·m). Magnetic field strength H is expressed in Amperes per meter (A/m), directly reflecting the electric current driving an electromagnetic coil.
CGS Standard: Gauss (G) & Oersted (Oe)
1 Tesla = 10,000 Gauss. In free space (vacuum), where relative permeability is unity, an applied field of 1 Oersted produces exactly 1 Gauss of flux density.
Superconducting Solenoids & MRI Safety
Clinical magnetic resonance imaging (MRI) instruments utilize niobium-titanium (NbTi) superconducting coils cooled to 4 Kelvin by liquid helium to generate continuous fields of 1.5T to 3.0T without resistive electrical dissipation. Strict safety perimeters (the 5-Gauss line) prevent ferromagnetic projectile accidents.