What Are Field Lines in Vector Fields?

[imy786]

Homework Statement

describe what field lines are (7 marks)

Homework Equations

The Attempt at a Solution

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.

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 exactly equivalent to a complete description of the vector field itself.

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.

 

[hage567]

Are you handing this in as the answer to an assignment? I don't believe that you wrote this yourself.

EDIT: It appears you didn't. http://en.wikipedia.org/wiki/Field_line

 

[malawi_glenn]

hehe lol, that was the worst I ever seen

 

[bidhati]

Field lines are a visual representation of a vector field.
The lines represent the direction, and strength of the field. In an electric field field
lines flow from a positive charge and into a negative charge, in the case of a
gravitational field field lines start at infinity and end at a mass point. The direction of
the field line is indicated by an arrow which points in the direction of the field line.
The strength of the field is indicated by the density of the field lines. Where the field
is strongest the lines will be closer together and thus where the field is weaker the
field lines will be further apart. In reality fields are three dimensional but this is hard
to depict so generally field lines are drawn in 2 dimensions but still represent a 3
dimensional field.