Editing Magnetic field (section)

=== Visualization{{anchor|Magnetic field line}}===
{{Main|Field line}}

{{Multiple image|header=Visualizing magnetic fields
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|image1=Magnet0873.png | alt1= |caption1=
|image2=Magnetic field near pole.svg | alt2= |caption2=
|footer=Left: the direction of magnetic [[field line]]s represented by [[iron filings]] sprinkled on paper placed above a bar magnet.<br>
Right: [[compass]] needles point in the direction of the local magnetic field, towards a magnet's south pole and away from its north pole.
}}

The field can be visualized by a set of ''magnetic field lines'', that follow the direction of the field at each point. The lines can be constructed by measuring the strength and direction of the magnetic field at a large number of points (or at every point in space). Then, mark each location with an arrow (called a [[vector (geometry)|vector]]) pointing in the direction of the local magnetic field with its magnitude proportional to the strength of the magnetic field. Connecting these arrows then forms a set of magnetic field lines. The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and the local density of field lines can be made proportional to its strength. Magnetic field lines are like [[Streamlines, streaklines, and pathlines|streamlines]] in [[Fluid dynamics|fluid flow]], in that they represent a continuous distribution, and a different resolution would show more or fewer lines.

An advantage of using magnetic field lines as a representation is that many laws of magnetism (and electromagnetism) can be stated completely and concisely using simple concepts such as the "number" of field lines through a surface. These concepts can be quickly "translated" to their mathematical form. For example, the number of field lines through a given surface is the [[surface integral]] of the magnetic field.<ref name="purcell2ed"/>{{rp|p=237}}

Various phenomena "display" magnetic field lines as though the field lines were physical phenomena. For example, iron filings placed in a magnetic field form lines that correspond to "field lines".<ref group="note" name="ex07">The use of iron filings to display a field presents something of an exception to this picture; the filings alter the magnetic field so that it is much larger along the "lines" of iron, because of the large [[magnetic permeability|permeability]] of iron relative to air.</ref> Magnetic field "lines" are also visually displayed in [[Aurora (astronomy)|polar auroras]], in which [[Plasma (physics)|plasma]] particle dipole interactions create visible streaks of light that line up with the local direction of Earth's magnetic field.

Field lines can be used as a qualitative tool to visualize magnetic forces. In [[ferromagnetic]] substances like [[iron]] and in plasmas, magnetic forces can be understood by imagining that the field lines exert a [[Maxwell stress tensor|tension]], (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines. "Unlike" poles of magnets attract because they are linked by many field lines; "like" poles repel because their field lines do not meet, but run parallel, pushing on each other.<!-- Note: this last "explanation" is purely pedagogical, without technical substance and should be improved. -->