Field strength

The field strength is a physical quantity used to describe fields . The term field strength is particularly common for vector fields such as electric and magnetic fields. Here the field strength can be clearly defined using the force that the field exerts on a test specimen .

In classical field theories, field strengths are described by vectors or tensors or, more generally, by differential forms ; Occasionally the amount or - especially to characterize alternating electrical fields - the effective value of a field strength vector is referred to as field strength. In quantum field theories , field strengths are treated as quantum mechanical observables and are therefore represented as operators .

The four basic forces of physics are also described in field theories using the field strength concept. In today's (2017) theories, the field strength is defined as the curvature of a calibration potential .

The spatial distribution and the temporal development of the field strength result from field equations that describe the relationship between field strength, interactions within the physical system under consideration and external source terms, e.g. B. map charges , flows or masses .

Operational definition

The operational definition (and thus the practical measurement specification) of the field strength is based on the force that the field exerts on a test specimen. The field strengths of the weak and strong interaction are not directly measurable quantities, so there is no operational definition for them.

Electric field strength

Field strength vectors of an electric field at selected points. The vectors point away from the positive charge (red) towards the negative charge (green). Their length is a measure of the local field strength.

→ Main article : Electric field strength

If a resting body carries the charge and experiences an electrical force , then the electrical field strength prevails at this point ${\displaystyle Q}$ ${\displaystyle {\vec {F}}}$

${\displaystyle {\vec {E}}={\frac {\vec {F}}{Q}}}$.

The electric field strength can be specified in the units Newton ( ) per Coulomb ( ) or Volt ( ) per meter ( ): ${\displaystyle \mathrm {N} }$ ${\displaystyle \mathrm {C} }$ ${\displaystyle \mathrm {V} }$ ${\displaystyle \mathrm {m} }$

${\displaystyle [E]=\mathrm {{\frac {N}{C}}={\frac {V}{m}}} }$

Magnetic field

→ Main articles : Magnetic flux density  and magnetic field strength

For historical reasons, the designation of vector magnetic field quantities is not consistent with the otherwise consistent use of the term field strength. The magnetic analogue of the electric field strength is not the magnetic field strength , but the quantity called the magnetic flux density . Therefore, in the electromagnetic field strength tensor, the electrical field strength and the magnetic flux density are physically meaningful, but linguistically inconsistent . Some authors also deviate from the IUPAP recommendation and use the term “magnetic field strength”. ${\displaystyle {\vec {E}}}$ ${\displaystyle {\vec {H}}}$ ${\displaystyle {\vec {B}}}$ ${\displaystyle \,F^{\mu \nu }}$ ${\displaystyle {\vec {E}}}$ ${\displaystyle {\vec {B}}}$ ${\displaystyle {\vec {B}}}$

The magnetic flux density is defined by the Lorentz force experienced by a charge Q moving with the speed in a magnetic field: ${\displaystyle {\vec {B}}}$ ${\displaystyle {\vec {F}}}$ ${\displaystyle {\vec {v}}}$

${\displaystyle {\vec {F}}=Q\left({\vec {v}}\times {\vec {B}}\right).}$

The SI unit of is the Tesla with the symbol T: ${\displaystyle {\vec {B}}}$

${\displaystyle \left[B\right]={\frac {\mathrm {N} }{\mathrm {Am} }}=\mathrm {T} }$

Gravitational field strength

→ Main article : Gravitational field

The gravitational field strength is the quantity that is obtained when the force acting in a gravitational field on a test mass is divided by the mass of the test mass: ${\displaystyle {\vec {g}}}$ ${\displaystyle {\vec {F}}}$ ${\displaystyle m_{\mathrm {P} }}$

${\displaystyle {\vec {g}}={\frac {1}{m_{\mathrm {P} }}}{\vec {F}}}$

For the gravitational field, the gravitational field strength at a location is, under certain conditions, the same as the acceleration due to gravity at that location .

As with acceleration , the unit of the gravitational field strength can be specified in meters per second squared ( ) or, when interpreted as a force field , in Newtons per kilogram ( ): ${\displaystyle \mathrm {m} /\mathrm {s^{2}} }$ ${\displaystyle \mathrm {N} /\mathrm {kg} }$

${\displaystyle [g]=\mathrm {{\frac {m}{s^{2}}}={\frac {N}{kg}}} }$

The field strength as the curvature of a calibration potential

→ Main article : Gauge theory

In modern field theories, e.g. B. the Yang-Mills theory , the field strength is not defined operationally, but derived mathematically from the basic equations of the theory. In these theories, field strength is defined as the curvature of a calibration potential. This definition clearly determines the field strength for a given calibration potential, but the reverse assignment of the field strength to the calibration potential is not unambiguous, the effect and the field strength are invariant under calibration transformations of the calibration potential.

Since the electromagnetic field strength and the gravitational field strength can be measured directly, the field strength was regarded as the most physically relevant field quantity until the 1960s. Today, however, many field theorists regard the calibration potential as the more fundamental quantity compared to the field strength. One reason for this are physical effects such as the Aharonov-Bohm effect , which can only be described by the magnetic vector potential and not by the field strength tensor. Also, the gauge symmetries that are fundamental for the formulation of gauge theories are only expressed at the level of the gauge potentials and not at the level of the field strength.

literature

• F. Scheck, Theoretical Physics 3: Classical Field Theory. From electrodynamics to gauge theories. , 2nd edition, Springer, Berlin, 2005, ISBN 3-540-42276-5 , ISBN 978-3-540-23145-5 .
• M. Burgess, Classical Covariant Fields , Cambridge University Press, 2002, ISBN 0-521-81363-8 .

Individual evidence

1. ^ "Note that the field strength (of non-Abelian fields) is not gauge-invariant: it transforms in a non-trivial way. This means that is not an observable in non-Abelian field theory. "M. Burgess, Classical covariant fields , Cambridge University Press, 2002, p. 470. ${\displaystyle F_{\mu \nu }}$
2. ↑ D. Meschede, Gerthsen Physik , 23rd edition, Springer, 2006, p. 296. google books
3. ↑ "According to today's approach, the name" magnetic field strength "is misleading because it describes the effect of the field, i.e. H. the force effect is expressed, but [...] is described by the magnetic flux density. ”: H. Frohne et al., Moeller Fundamentals of Electrical Engineering , Vieweg + Teubner, 2008, p. 203. google books
4. ↑ "The mechanical force divided by (the magnetic pole strength) P would best be called" magnetic field strength ". But we will often follow the common usage and call this quantity "magnetic induction B" ”: A. Sommerfeld, lectures on theoretical physics: Elektrodynamik , Verlag Harri Deutsch, 2001, p. 10. google books
5. ↑ Since there is now agreement that B is the "correct" magnetic field strength and should actually be called that, and will probably soon be called that, we use the term "magnetic field strength" for B, in deviation from the IUPAP recommendation: W. Raith, C. Schaefer, Textbook of Experimental Physics, Vol. 2, Elektromagnetismus , Gruyter, 1999, p. 123 below. google books
6. ^ D. Meschede, Gerthsen Physik , 23rd edition, Springer, 2006, p. 348. google books
7. ↑ ^{a b} D. Meschede, Gerthsen Physik , 23rd edition, Springer, 2006, p. 48. google books
8. ↑ "The traditional view took F as physically real, responsible for observable effects, and giving an intrinsic and complete description of electromagnetism. In contrast, the potential A was taken only as auxiliary and fictitious, without physical reality, because it was thought to be arbitrary and unable to produce any observable effect. ": TY Cao, Conceptual developments of 20th century field theories , Cambridge University Press, 1998, p. 306. google books
9. ^ Y. Nagashima, Y. Nambu, Elementary Particle Physics: Volume 1: Quantum Field Theory and Particles , Wiley, 2010, p. 747.