Magnetic Field - Definitions, Units, and Measurement

Definitions, Units, and Measurement

The magnetic field can be defined in several equivalent ways based on the effects it has on its environment.

Often the magnetic field is defined by the force it exerts on a moving charged particle. It is known from experiments in electrostatics that a particle of charge q in an electric field E experiences a force F = qE. However, electrostatics alone is insufficient to explain the force a charged particle experiences in other situations, such as when it moves in the vicinity of a current-carrying wire. In these situations, the force can be correctly accounted for if one introduces a vector B and then writes down a new equation for the force, known as the Lorentz force law:

Here v is the particle's velocity and × denotes the cross product. The vector B is termed the magnetic field, and it is defined as the vector field necessary to make the Lorentz force law correctly describe the motion of a charged particle. This definition allows one to determine B in the following way, as described by Purcell:

he command, "Measure the direction of magnitude of the vector B at such and such a place," calls for the following operations: Take a particle of known charge q. Measure the force on q at rest, to determine E. Then measure the force on the particle when its velocity is v; repeat with v in some other direction. Now find a B that will make fit all these results; that is the magnetic field at the place in question.

Alternatively, the magnetic field can be defined in terms of the torque it produces on a magnetic dipole (see magnetic torque on permanent magnets below).

Devices used to measure the local magnetic field are called magnetometers. Important classes of magnetometers include using a rotating coil, Hall effect magnetometers, NMR magnetometers, SQUID magnetometers, and fluxgate magnetometers. The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around a field line produce synchrotron radiation which is detectable in radio waves.

Alternative names for B
Magnetic flux density Magnetic induction Magnetic field
Alternative names for H
Magnetic field intensity Magnetic field strength Magnetic field Magnetizing field

There are two magnetic fields, H and B. In a vacuum they are indistinguishable, differing only by a multiplicative constant that depends on the physical units. Inside a material they are different (see H and B inside and outside of magnetic materials). The term magnetic field is historically reserved for H while using other terms for B. Informally, though, and formally for some recent textbooks mostly in physics, the term 'magnetic field' is used to describe B as well as or in place of H. There are many alternative names for both (see sidebar).

In SI units, B is measured in teslas (symbol: T) and correspondingly Φ_B (magnetic flux) is measured in webers (symbol: Wb) so that a flux density of 1 Wb/m2 is 1 tesla. The SI unit of tesla is equivalent to (newton·second)/(coulomb·metre). In Gaussian-cgs units, B is measured in gauss (symbol: G). (The conversion is 1 T = 10,000 G.) The H-field is measured in ampere per metre (A/m) in SI units, and in oersteds (Oe) in cgs units.

The smallest precision level for a magnetic field measurement is on the order of attoteslas (10−18 tesla); the largest magnetic field produced in a laboratory is 2.8 kT (VNIIEF in Sarov, Russia, 1998). The magnetic field of some astronomical objects such as magnetars are much higher; magnetars range from 0.1 to 100 GT (108 to 1011 T). See orders of magnitude (magnetic field).