Field line

Field line

A field line is a locus that is defined by a vector field and a starting location within the field. A vector field defines a direction at all points in space; a field line may be constructed by tracing a path in the direction of the vector field. More precisely, the tangent line to the path at each point is required to be parallel to the vector field at that point.

Field lines are useful for visualizing vector fields, which consist of a separate individual vector for every location in space. If the vector field describes a velocity field, then the field lines follow stream lines in the flow. Perhaps the most familiar example of a vector field described by field lines is the magnetic field, which is often depicted using field lines emanating from a magnet.

A complete description of the geometry of all the field lines of a vector field is sufficient to completely specify the "direction" of the vector field everywhere. In order to also depict the "magnitude", a selection of field lines is drawn such that the density of field lines (number of field lines per unit area) at any location is proportional to the magnitude of the vector field at that point.

Field lines can be used to trace familiar quantities from vector calculus: divergence may be seen as a net geometric divergence of field lines away from (or convergence toward) a small region, and the curl may be seen as a helical shape of field lines.

While field lines are a "mere" mathematical construction, in some circumstance they take on physical significance. In the context of plasma physics, electrons or ions that happen to be on the same field line interact strongly, while particles on different field lines in general do not interact.

References

*cite book | author=Griffiths, David J. | title=Introduction to Electrodynamics (3rd ed.) | publisher=Prentice Hall | year=1998 | id=ISBN 0-13-805326-X | page=pages 65-67 and 232

See also

* Force field (physics)
* External ray — field lines of Douady-Hubbard potential of Mandelbrot set or filled-in Julia sets
* Line of force


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  • field line — noun an imaginary line in a field of force; direction of the line at any point is the direction of the force at that point • Syn: ↑line of force • Hypernyms: ↑line • Hyponyms: ↑electrical line of force, ↑magnetic line of force * * * …   Useful english dictionary

  • field line — noun A line of constant strength in a field …   Wiktionary

  • field line — Physics. See line of force. * * * …   Universalium

  • electric field line — elektrinė jėgų linija statusas T sritis fizika atitikmenys: angl. electric field line vok. elektrische Kraftlinie, f rus. электрическая силовая линия, f pranc. ligne de force électrique, f …   Fizikos terminų žodynas

  • line of flux — field line …   Useful english dictionary

  • line of force — noun an imaginary line in a field of force; direction of the line at any point is the direction of the force at that point • Syn: ↑field line • Hypernyms: ↑line • Hyponyms: ↑electrical line of force, ↑magnetic line of force * * * …   Useful english dictionary

  • Line of force — A line of force in Faraday s extended sense is synonymous with Maxwell s line of induction. [ 1907 Encyclopedia Britannica, [http://books.google.com/books?id=PAgEAAAAYAAJ pg=PA64 dq=%22Line+of+force%22 as brr=3 page 64] ] According to J.J.… …   Wikipedia

  • line of force — Physics. an imaginary line or curve in a field of force, as an electric field, such that the direction of the line at any point is that of the force in the field at that point. Also called field line. [1870 75] * * * …   Universalium

  • line of induction — a field line in a field of magnetic induction * * * (formerly) a line of force in a magnetic field …   Useful english dictionary

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