Visualizing the "Magnetic Flux Ropes" and "Reconnection"

[MGmirkin]

(IMAGE and Cluster View "Magnetic Reconnection")
http://svs.gsfc.nasa.gov/vis/a010000/a0 ... index.html
http://svs.gsfc.nasa.gov/vis/a010000/a0 ... gClstl.mpg

The IMAGE and Cluster spacecraft were ideally positioned in their orbits to view the reconnection event which led to the proton aurora formation.

My jaw about dropped when I saw this animation. It's oversimplified, of course... But, a GREAT animation nonetheless!

I assume that the little points flying around, following the solid lines are the "charged particles" following "field lines" (field-aligned current)?

(Proton Aurora)
http://svs.gsfc.nasa.gov/vis/a010000/a0 ... index.html

(How's this for a "flux rope?")
http://svs.gsfc.nasa.gov/vis/a010000/a0 ... still6.tif

Cheers,
~Michael Gmirkin

See also: my recent post on WATCH THIS MOVIE! BIRKELAND CURRENTS VERIFIED

[upriver]

Of course here is what a reconnection really looks like in a lab.



From the large plasma device in LA.
http://plasma.physics.ucla.edu/bapsf/pages/gallery.html

[StefanR]

Laboratory-generated plasma evolves from flux rope to mini helix. Photo from Thomas Intrator, P-24

At the Sun's edge, in a region called the heliosphere, magnetic fields and electrical currents constantly align and twist themselves in massive 3-D structures called "magnetic flux ropes." These high-tension ropes are unstable and tend to kink and relax into helical configurations (through what theorists call the kink instability). Occasionally, a rope end—which was previously "tied" to the Sun's surface—breaks loose, ejecting electrically charged gas called plasma and producing solar flares that can wreak havoc with everything from satellites to electrical power grids.

Once observed only in places like the Sun's surface, flux ropes are now being created by Los Alamos scientists in the laboratory, making it possible to tie experimental data to prior theoretical analyses. As reported in the July 7, 2006, Physical Review Letters, a small plasma gun shoots plasma into a vacuum. The plasma then flows along an externally produced magnetic field to form plasma-current filaments, or flexible wires composed of plasma. These "mini flux ropes" are photographed and studied with probe measurements as they wind helically around an imaginary central axis (see photo sequence at left).

This close-up study can shed light on the effects of flux ropes in everything from the Earth's magnetosphere to the giant astrophysical jets and radio lobes associated with active galaxies throughout the universe. According to Los Alamos experimentalist Thomas Intrator, "The more we learn in the laboratory, the more we'll know about how solar flares are produced and how the energy locked up in magnetic fields affects the large-scale structure of the universe." (see also http://arxiv.org/pdf/physics/0608263 )

http://www.lanl.gov/science/1663/spotlight.php

False color images of single and multiple flux ropes in hydrogen plasma reveal helically twisted structures. Images taken with the dicam pro intensified CCD camera. Experiments were performed in the Reconnection Scaling Experiment (RSX) at Los Alamos National Laboratory. Courtesy of Ivo Furno, P-24 Plasma Physics Group, Los Alamos National Laboratory

http://www.pco.de/pco/php/library/image ... %20IMAGING

[MGmirkin]

Interesting stuff, StefanR... Quite timely, too. Thanks!

I've added it to a recent article.

~Michael Gmirkin

[StefanR]

Our group's research emphasizes close coupling between experimental and theoretical plasma physics, both fundamental and applied. Typically, unexpected experimental results motivate new theoretical interpretations, or a new theory suggests a new experimental interpretation. Our research spans several different areas of plasma physics that share related concepts. In particular, we are investigating spheromak plasmas, a configuration that provides a possible low-cost path for magnetically confined fusion energy that could ultimately provide electric power for a city. The physics of spheromak formation is related to the physics of solar corona loops and to astrophysical jets because spheromaks, coronal loops, and astrophysical jets are governed by essentially the same set of magnetohydrodynamic equations and differ only in boundary conditions.

"Spider-leg" formation of eight plasma-filled magnetic flux tubes. The inner parts of the legs coalesce in approximately 1 microsecond to form a plasma jet moving at 30-50 km/sec.

http://www.aph.caltech.edu/people/bellan_p.html

[StefanR]

Maybe it's better to put the complete sequence here:

Plasma Jets on Earth

From the surface of the sun to the violent cores of quasars, many astrophysical objects shoot plasma in sharply defined streams, guided by magnetic fields. In the 22 July PRL, researchers present a laboratory demonstration in which magnetic forces squeeze hot plasma into a narrow tube without any extraordinary arrangement of conditions. This mechanism, the scientists claim, may help explain why tightly confined jets arise in many different astrophysical circumstances, although some astrophysicists find the leap from lab to cosmos premature.

Jet plane. Electric and magnetic fields applied to a disk and ring create a "spider" pattern of plasma. Over time, the streams merge at the center into a single jet that is reminiscent of jets shooting from quasars or the sun.

A plasma is a gas whose atoms have separated into a mix of charged ions and electrons. Its behavior in a magnetic field is complex, but there are some basic principles. Magnetic field lines cannot move through the plasma without generating electric forces that resist the motion. So the charged particles are "stuck" to the magnetic field lines and can only move along them, as when an electric current flows in the plasma. In addition, just as two adjacent wires carrying current are magnetically attracted to one another, so currents flowing in a plasma try to squeeze together, pulling in magnetic field lines and plasma with them.
Paul Bellan of the California Institute of Technology has theorized that this tendency of currents to draw plasma into so-called magnetic flux tubes is even stronger than others have assumed. When field lines flare like the bell of a trumpet, he says, compressive magnetic forces not only narrow the bell, but they also move plasma along the tube and create a more uniform, cylindrical arrangement of plasma and field lines. Moreover, the same forces draw external matter into the constricting tube, further increasing the plasma density.
In laboratory experiments, Bellan and his colleagues have now demonstrated key elements of this theory. In a vacuum chamber, they placed a metal ring around a metal disk, leaving a gap between the two. They generated an enveloping magnetic field with a large coil and set up a voltage difference between the disk and ring.

The researchers injected gas into 16 nozzles located at eight equally spaced points around the ring and disk. A "spider leg" pattern of plasma appeared, following the magnetic field's geometry, with eight arched tubes--each one connecting a nozzle near the disk center with the adjacent one on the ring. But the pattern rapidly evolved. Current flow along the "legs" narrowed their cross section, while causing a dramatic increase in the plasma density. Then the central portions of the eight arches merged into a single jet shooting outwards from the disk, as the arches thinned. The experiment lasted some ten microseconds, with the central jet narrowing further before succumbing to instabilities.

Because there is evidence for current flows in many astrophysical situations, Bellan argues that this mechanism for producing a tightly collimated jet could apply widely. But Eric Priest, of St. Andrew's University in Scotland, while admiring the Caltech team's demonstration, finds its astrophysical applicability not at all obvious. He worries in particular that the timescale of the experiment may not scale up appropriately to solar and astrophysical values. Adam Frank of the University of Rochester, New York, cautions that the behavior of astrophysical jets depends on additional factors, such as the ratio of thermal energy to magnetic energy, that laboratory experiments may not mimic.

Bellan responds that plasmas show consistent behavior under a broad range of conditions, and that scaling arguments for the spatial extent, velocity, and timescale of jets can be foundWhen he has lectured on this work, he says, "astrophysicists don't give me a hard time.".

http://focus.aps.org/story/v16/st4

[MGmirkin]

Recall having seen these images before, probably on the prior "Thunderbolts Forum 1.0"

I note they still seem to be stuck in "frozen-in field lines" mode, talking of "dragging" magnetic field lines, as though the field lines are real entities that can br "dragged" around, snapped, reconnected, etc.

As opposed to the magnetic fields being GENERATED BYPRODUCTS of electric currents, per electromagnetic field theory:

http://hyperphysics.phy-astr.gsu.edu/hb ... agfie.html
http://www-istp.gsfc.nasa.gov/Education/wmfield.html
http://www.who.int/peh-emf/about/WhatisEMF/en/
http://en.wikipedia.org/wiki/Electromagnetic_field

Otherwise, quite interesting.

Regards,
~Michael Gmirkin

[junglelord]

That helix structure is a longitudinal form. That is fundamental. It is a scalar form. It is scaleable and is the archetype form from non material aether structure up to spiral galaxy's, so those little birkeland currents they made, they are fundamental. If you really understand comparative methodology its very clear what nature is saying at all levels.
Magnetic flux tubes are also fundamental in quantum systems. The magnetic flux tube reminds me of an extended soap bubble or smoke ring, a soliton, which is a non linear coherent wave, a scalar, with a helix longitudinal scalar rope inside it. So that is the two fundamental longitudinal forms we all know anyway. Did you realize that the double loxosome of the APM aether unit is at least to me a magnetic flux tube.

Another thing nature told me, Double layers always make the vortex....always.

Yet people have no clue about these simple truths

[StefanR]

This laboratory simulation of solar prominences is based on the premise that the physics of erupting solar prominences is analogous to the physics of the formation of laboratory spheromaks. The image to the left shows a photo of a simulation of a prominence obtained in our lab. Distance between footpoints is approximately 10 cm. Diagnostics include a high speed camera and measurements of magnetic flux, current , and voltage.

http://ve4xm.caltech.edu/Bellan_plasma_ ... borato.htm

[StefanR]

SOLAR PROMINENCES

Prominences are huge clouds of gas which are often seen on or above the
solar limb, and are the easiest H-alpha emission feature to observe,
requiring a filter passband that can be one or two Angstroms wide.
Prominences observed on the solar disk are the darker features known as
Filaments, and need a passband width under one Angstrom in order to be
clearly visible. They often represent a sheared magnetic field boundary or
neutral line between opposite polarities where gas is trapped around bunched
field lines. The forms prominences can take vary widely, but the following
general scheme (Zirin) is somewhat useful in categorizing them:

CLASS 1: QUIESCENT FILAMENTS/PROMINENCES (long lived, fairly static)
a. QRF (Quiet Region Filament) ie: hedgerow, curtains, floating arches,
arcs, fans, ect.
b. ASCENDING PROMINENCES (end of the quiescent phase) "Disparition
Brusque" ("lifting off") eruption.
c. ARF (Active Region Filament): a filament in or near an active region
(netural line filaments).

CLASS 2: ACTIVE FILAMENTS/PROMINENCES (short-lived, moving)
a. LIMB FLARES (bright blobs, sometimes expanding into eruptive
prominences).
b. SURGES: collimated ejected material previously not seen (very sudden
jet of gas).
c. SPRAYS: uncollimated ejecta previously visible as pre-flare elevated
features (violent explosion).
d. FLARE LOOPS and CORONAL RAIN (often post-flare ejecta or other gas).



QUIESCENT PROMINENCES/FILAMENTS take a wide variety of forms, and tend to be
much longer than they are wide. Quiet Region Filaments (QRFs) are some of
the largest and longest lasting quiescents, with a few being visible for
several solar rotations. They are most often found where there is little
major activity such as the so-called "Polar Crown" high latitude areas,
although they may sometimes be found between or even near active regions.
The Hedgerow prominence is a fairly common QRF, and tends to look like an
irregular row of bushes. Hedgerows tend to be highly detailed, with
considerable branching and fine structure being visible at high resolution.
QRFs appear in many other forms, including floating arches, fans, curtains,
large curving blades, flames, and magnificent spiderweb-like arcs. Many have
upper edges that tend to be sharper than their lower sides, which can be
irregular or scalloped in form. Motion of material in QRFs is usually slow
and small in scale, leaving the overall prominence shape unchanged, but minor
changes can occasionally be seen in as little as 10 minutes. When viewed on
the solar disk, QRFs tend to lose some of their fine detail, becoming faint
irregular dark patches or large gently curving arcs of dark matter.
Prominences are darker on the disk because they absorb light from below and
then re-emit it in all directions. Some low-level filaments will often show
a brighter base due to a "blanketing" effect they have which reduces the
emission losses of the lower chromosphere.
Large Quiescents are not always stable, and if they exceed a height of
50,000 km above the surface (0.07 solar radii), they will usually break loose
from the sun within 48 hours in an eruption known as a "Disparition Brusque"
(sudden vanishing). Disparition Brusque eruptions usually last less than one
or two hours. They vary in form from a simple fading away of the quiescent,
to a spectacular "lifting off", where the prominence rises up and drifts away
from the sun, slowly breaking up in the process. Mild surface brightening
can also occasionally occur. Sometimes, a vanished quiescent will even
reform a few hours or days later near its previous location. In a few large
eruptions, a Dispartition Brusque can produce a Coronal Mass Ejection. Some
prominences do rotate slowly, and a few even look and act like tornadoes,
especially Disparition Brusque debris.
Active Region Filaments (ARF's) (best seen on the solar disk) tend to be
smaller, darker, and narrower than their giant cousins, the QRFs. They are
present in or near active regions and sometimes wind around or even through
large sunspot groups. The Neutral Line Filament in an active region under-
going the shearing of local magnetic fields is an example of an ARF. Arch
Filament System "filaments" between forming sunspots are really fibrils,
tending to be small and fairly short-lived unless flux emergence goes on for
very long. They can be particularly dark when a spot is emerging, and often
show Doppler shifts from material flowing in the fibrils.

ACTIVE FILAMENTS/PROMINENCES are short-lived features associated with
solar flares and other violent events. Limb Flares can appear on the solar
limb as elevated bright blobs. Occasionally, a small ARF in which a flare
begins will rise and expand into a majestic Eruptive Prominence, often in the
form of a twisting loop, while intense emission appears on the surface.
Flares sometimes produce a SURGE Prominence, visible near the limb as a well
defined jet of bright gas, and which can occasionally be seen in emission on
the solar disk.




These jets sometimes take the form of fine closely-spaced
spines which may be visible up to a solar radii from the limb. Surges can
also be seen as bright-based narrow dark features on the disk of the sun
(sometimes blue-shifted). Surges usually happen when a small satellite spot
of opposite magnetic polarity comes up in or very close to the penumbra of a
big regular sunspot. A small flare then occurs, resulting in an outward
ejection of gas which is confined into a narrow stream by the dominant spot's
field. The surge ejecta's velocity (50-200 km/sec) isn't enough to leave
the sun, and the gas will follow magnetic field lines as it falls or draws
back, sometimes creating a "splash" of brightening near the point of origin.
Much smaller non-flare surges can often be seen in active and occasionally in
Ephemeral regions on the solar disk as tiny blue-shifted "smoke stack" or
"puff" filaments, which resemble a smoke plume. Smoke stack surges usually
last only a few minutes, and can occasionally occur in the middle of a fairly
quiet area, especially in the early stages of an Emerging Flux Region.
Another active prominence type, usually resulting from the most violent
flares, is the SPRAY, a spectacular uncollimated expansion of disrupted ARF
material, sending debris flying off in many directions at speeds of 200-300
km/sec or more (up to 2000 km/sec for some of the largest flares). Often, the
filament involved becomes slightly elevated initially, then it explodes
outward in the spray. Motion of spray material can often be seen in only a
few minutes time, and occasionally, material can be seen leaving the sun
entirely (Coronal Mass Ejection).
Two other types of flare-associated active prominences are the Flare
Loops, and Coronal Rain. FLARE LOOPS are large thin circular or elliptical
vertical loops of gas which appear in the later stages or after a major
flare. They tend to be brighter at the top and at their bases, and often
show a nested structure of many very thin loops (Arcades), all with nearby
endpoints. These loops are where flare ejecta or other gas has encountered
the new magnetic field lines set up by the reconnection which occurs during
the flare. Motion of material can often be seen down both sides of the loop
towards the surface. The first loops form fairly low, while succeeding loops
form higher and higher above the surface. Flare loops are sometimes not seen
after some explosive flares or with small flares. They usually last only a
matter of hours, and should not be confused with the quiescent "Floating
Arches" prominences, which are thick or irregular in form, and are much
longer lived. CORONAL RAIN is the diffuse faint patchy emission from gas
descending back towards the surface as it encounters magnetic field lines.
It can often be seen often as material "raining" down into post-flare loops
or active regions.

SUNSPOT GROUP DEVELOPMENT SEQUENCE: In white light, an early indication
of a developing sunspot group is often the appearance of a few tiny pores,
sometimes separated by a short distance, and possibly accompanied by faculae.
In H-alpha, a bipolar group begins as a small bright oval area of plage with
a few small surges. Several hours later, the pores and Arch Filament System
(AFS) superimposed on very bright plage begin to appear, forming what is
known as an Emerging Flux Region (EFR). The AFS often takes the form of
several closely spaced fine filaments that arch between the emerging magnetic
flux tube's poles (often marked by pores), tracing out the field lines like
those of a bar magnet. These AFS filaments show upward motion (blue shift)
at the tops and downward flow at the ends (red shift). Small bright points
of H-alpha emission lasting only a few minutes known as Ellerman Bombs can
often be seen near the middle of the EFR. Rapid EFR growth then follows with
some of the pores intensifying or merging to form the first sunspot umbras.
Usually, the (p), or preceding polarity spot will form first and then move
westward relative to the following (f) polarity spot (spot "Proper Motion")
to the eventual head of the group at about 1 km/sec. One to two days after
formation, the first spots frequently form penumbras, their proper motion
stops or slows, and the arch filaments connected to them usually disappear or
erupt upward. The (p) spots may continue to move westward as long as new flux
continues to emerge (this usually leaves some plage and a limited AFS near
the center of the group where a few more pores or spots might eventually
form). *Bright plage with arch filaments are good signs of continuing
emerging magnetic flux.* (f) spots will either remain relatively fixed or
will drift slightly eastward. In large active spot groups, the (f) spots may
occasionally continue to develop until they rival the (p) spots in size.
Sometimes, a (p) spot will develop accompanied by only bright plage and a few
small filaments instead of trailing spots (Alpha group). Plage is rarely
seen ahead of the (p) spots unless satellite opposite polarity is emerging.
If small emerging flux regions emerge offset from the central AFS axis, a
finger of plage forms extending to the new pole until its fields reconnect.
If the EFR comes up deep inside a plage, the opposite polarity spot will be
surrounded by Field Transition Arch fibrils connecting to the plage. Beta
groups often form when only one or two adjacent flux tubes with the same
orientation come up together. Extended groups can form from from the
emergence of several dipoles end to end, sometimes yielding Beta-Gammas if
polarities are mixed. Multiple flux tubes emerging fairly closely together
in sequence or tilted to each other can form Gamma or Delta groups.



As magnetic flux emergence ceases, the individual spots of the dipole(s)
frequently interact with local fields and other spots, behaving as if they
had never been connected to each other. The main dominant spot will often
form magnetic connections to distant fields, sometimes forming a "moat"
around itself consisting of a thin patchy ring of brightening and a group of
nearly radial H-alpha fibrils roughly twice the penumbral width. Once the
active region becomes "mature" (reaches maximum longitudinal spread), it will
tend to slowly decline and fade away unless more flux emerges to keep it
alive. Mature spots rarely move very much, nor do they show much activity
unless new flux emerges nearby. The spot motion that leads to magnetic shear
and flares is almost always in an Emerging Flux Region. However, flux is
somewhat more likely to emerge near where it has previously emerged, so even
mature spots bear a little watching. Normal EFR development results in a
fairly peaceful spot group which may have produced a few minor flares. After
a few quiet weeks of existence, its spots usually shrink and decay into two
diffuse unipolar areas, sometimes marked by weak H-alpha brightening and/or a
filament. In declining groups, the smaller f polarity spots usually vanish
before the dominant spots begin to decay. Most groups finally decay into a
single p spot with no plage, which then slowly shrinks and dies out.

http://www.prairieastronomyclub.org/halpha/

[StefanR]

Thin auroral arcs 100-1000 m width (possibly related to Alfvenic structures) pictured by Trond Trondsen.

Project Objectives:
High time resolution measurements performed in ionospheric/magnetospheric plasma provide growing evidence that thin auroral forms with thickness of ~1 km are related to solitary electromagnetic structures of similar thickness. These structures are most clearly observed in data from medium altitude satellites, as for example Freja at h~1500 km, and are associated with strong electric fields, field-aligned currents, large electron energy fluxes, density depletions, and a wealth of high frequency waves. The electromagnetic structures are being explained in the literature by a number of competing theoretical models as for example:
(1) dispersive field line resonances
(2) solitary kinetic Alfven waves
(3) nonlinear Alfven solitons
(4) magnetic field line fractures
(5) vortex street structures
(6) Alfvenic shocks
(7) drift Alfven waves
(8) Alfven resonance cones.
This indicates great uncertainty and insufficient understanding of the fundamentals of the ionosphere-magnetosphere coupling. The measurements gathered on satellites Viking, Freja, Polar, and Fast combined with high resolution ground based optical imagery, as for example ALIS facility in northern Scandinavia, portable auroral imager in Canada, provide invaluable experimental base for resolving some fundamental problems in auroral electrodynamics and the coupling between the magnetosphere and the ionosphere. In addition, a number of laboratory plasma devices, as for example LAPD facility in Los Angeles are being used in the parameter regime encountered in space, and provide important clues for understanding the plasma phenomena in space. The importance of Alfven waves for laboratory physics, space physics and astrophysics is that they represent a fundamental mode of transmitting information and electromagnetic energy througth magnetized plasmas.

http://cluster.irfu.se/ks/res/issi/index.html

[MGmirkin]

(Observing the Sun in H-Alpha)
http://www.prairieastronomyclub.org/halpha/

Once the active region becomes "mature" (reaches maximum longitudinal spread), it will tend to slowly decline and fade away unless more flux emerges to keep it alive.

Now why does that sound like the description of electric currents with respect to the magnetic fields?

Hmm, could it be that the magnetic fields only exist while a current is flowing. The time of "maturity" is the peak current flow, and once the current slows down or stops flowing the magnetic field dies off?

Say it ain't so!

(Wikipedia - Electromagnetic field)
http://en.wikipedia.org/wiki/Electromagnetic_field

The electromagnetic field is a physical field produced by electrically charged objects. It affects the behaviour of charged objects in the vicinity of the field.

[...]

The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law.

(What are electromagnetic fields?)
http://www.who.int/peh-emf/about/WhatisEMF/en/

Electric fields are created by differences in voltage: the higher the voltage, the stronger will be the resultant field. Magnetic fields are created when electric current flows: the greater the current, the stronger the magnetic field. An electric field will exist even when there is no current flowing. If current does flow, the strength of the magnetic field will vary with power consumption but the electric field strength will be constant.

(Wikipedia - Electric current)
http://en.wikipedia.org/wiki/Electric_c ... omagnetism

Electric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire.

Electric current can be directly measured with a galvanometer, but this method involves breaking the circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current.

It's all about the electrodynamics, people! Wake up, NASA! There's got to be an electrical engineer in the bunch, somewhere...

Regards,
~Michael Gmirkin

[StefanR]

It's all about the electrodynamics, people! Wake up, NASA! There's got to be an electrical engineer in the bunch, somewhere...

I sure do hope so. But I'm scared they don't know anymore what that is, an electric engineer. Most probable is they will send an IT-specialist for web-consulting.
But on the other hand, the only thing for most of us here is to learn how to do double-speak.

Magnetic flux:

The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element. More generally, magnetic flux is defined by a scalar product of the magnetic field and the area element vector.

The direction of the magnetic field vector is by definition from the south to the north pole of a magnet (within the magnet). Outside of the magnet, the field lines will go from north to south.

The magnetic flux through a surface is proportional to the number of magnetic field lines that pass through the surface. This is the net number, i.e. the number passing through in one direction, minus the number passing through in the other direction.

http://en.wikipedia.org/wiki/Magnetic_flux

Magnetic Flux
Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates. It is a quantity of convenience in the statement of Faraday's Law and in the discussion of objects like transformers and solenoids. In the case of an electric generator where the magnetic field penetrates a rotating coil, the area used in defining the flux is the projection of the coil area onto the plane perpendicular to the magnetic field.

http://hyperphysics.phy-astr.gsu.edu/Hb ... mg.html#c1

Electric flux

In electromagnetism, electric flux is flux of the electric field. Electric flux is proportional to the electric field lines going through a virtual surface.

http://en.wikipedia.org/wiki/Electric_flux

Electric Flux
The concept of electric flux is useful in association with Gauss' law. The electric flux through a planar area is defined as the electric field times the component of the area perpendicular to the field. If the area is not planar, then the evaluation of the flux generally requires an area integral since the angle will be continually changing.

http://hyperphysics.phy-astr.gsu.edu/Hb ... aw.html#c3


But I think one of the big obstacles is the use in science of field lines as actual entities, especially in popular/explanatory articles.
But as should be well known:

Equipotential Lines
Equipotential lines are like contour lines on a map which trace lines of equal altitude. In this case the "altitude" is electric potential or voltage. Equipotential lines are always perpendicular to the electric field. In three dimensions, the lines form equipotential surfaces. Movement along an equipotential surface requires no work because such movement is always perpendicular to the electric field.

http://hyperphysics.phy-astr.gsu.edu/hb ... uipot.html

And it probably is the same with magnetic field lines with main difference:

Magnetic field lines are very different from electric field lines because magnetic sources are inherently dipole sources with North and South magnetic poles. The magnetic field lines form closed loops and any closed surface will have a net zero number of lines leaving the surface.

http://hyperphysics.phy-astr.gsu.edu/hb ... orcon.html

[MGmirkin]

But on the other hand, the only thing for most of us here is to learn how to do double-speak.

But ma... I don't wanna' be a politician!

Regards,
~Michael Gmirkin