quantity

magnetic field strength

A measure of the magnitude of a magnetic field, determining its influence on charged particles.
16 related articles · 6 formulas

Description

Magnetic field strength is a measure of how intense a magnetic field is at a given point. It determines the force a moving charged particle experiences, the torque on a magnetic dipole, and the energy density stored in the field. In practical terms, it tells you how strongly a magnet will attract a paperclip or how much a particle's path will bend in a particle accelerator.

History

The concept evolved from early observations of lodestones and compass needles. The quantitative description was developed in the 19th century, with key contributions from André-Marie Ampère, who studied the forces between current-carrying wires, and James Clerk Maxwell, who unified electricity and magnetism in his equations in the 1860s.

How it works

The strength is typically quantified as a vector field, with both magnitude and direction. In the SI system, it is measured in teslas (T), where one tesla is one newton per ampere-meter. The force on a moving charge is given by the Lorentz force law, F = qv × B, where B is the magnetic flux density (often used interchangeably with field strength in most contexts). The field arises from moving charges, such as electric currents in wires or the intrinsic spin of electrons in magnetic materials.

In practice

Magnetic field strength is essential in designing MRI machines, particle accelerators like the LHC, and magnetic storage devices. It is also used in geophysics to map underground structures and in space missions to measure planetary magnetic fields.

Fun fact

The strongest magnetic field ever produced in a laboratory is about 1,200 teslas, created using an explosive technique called flux compression, which is strong enough to distort the shape of atoms.

Concept graph →

Formulas

$$\tau \propto B^2$$
Torque on a magnetic dipole is proportional to the square of the magnetic field strength.
What is in the formula
τvariableTorque on the magnetic dipole — torque newton metre
BvariableMagnetic field strength — magnetic field strength tesla
$$v_A = \frac{B}{\sqrt{4\pi \rho}}$$
Speed of transverse magnetohydrodynamic waves.
What is in the formula
v_AvariableAlfvén wave speed — velocity metre per second
Bvariablemagnetic field strength — magnetic field strength tesla
ρvariablemass density — mass density kilogram per cubic metre
$$\mathcal{L} = g_{a\gamma\gamma} a \mathbf{E} \cdot \mathbf{B}$$
Lagrangian term coupling axion to electromagnetic fields.
What is in the formula
avariableaxion field — axion field
Evariableelectric field — electric field volt per metre
Bvariablemagnetic field — magnetic field strength tesla
g_{aγγ}constantStrength of the interaction between axions and two photons. — axion photon coupling constant = model-dependent
$$B > v \sqrt{4\pi \rho}$$
Magnetic field strength required to balance kinetic energy density.
What is in the formula
BvariableMagnetic field strength — magnetic field strength tesla
vvariableCharacteristic velocity of plasma flow — velocity metre per second
ρvariableMass density of the plasma — mass density kilogram per cubic metre
√operatorTakes the square root of the argument — square root
$$E_c \propto \frac{|m_a^2 - \omega_{\rm pl}^2|}{B_\perp g_{a\gamma}}$$
Critical energy where axion-photon oscillations become energy-independent.
What is in the formula
E_cvariableCritical energy — energy joule
m_avariableAxion mass — mass kilogram
ω_plvariablePlasma frequency — angular frequency radian per second
B_perpvariablePerpendicular magnetic field strength — magnetic field strength tesla
g_aγvariableAxion-photon coupling constant — coupling constant inverse gev
$$l_{\rm osc} \propto \frac{\sqrt{1+(E_c/E_\gamma)^2}}{B_\perp g_{a\gamma}}$$
Length scale for periodic axion-photon conversion probability modulation.
What is in the formula
l_oscvariableOscillation length — length metre
E_cvariableCritical energy — energy joule
E_γvariablePhoton energy — energy joule
B_perpvariablePerpendicular magnetic field strength — magnetic field strength tesla
g_aγvariableAxion-photon coupling constant — coupling constant inverse gev

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