This is wrong. The GOES satellites are geo-synchronous, meaning they remain at continuous location with respect to the Earth. This also means that they are not in polar orbits. These satellites are similar to the LANL satellites but occupy the western hemisphere. You may be thinking of the DMSP satellites.

GOES is useful at measuring the magnetic fields. It does not, however, measure the ionospheric particles such as is done with the SuperDARN coherent scatter radars or the EISCAT or PFISR incoherent scatter radars. The group at the University of Saskatchewan has also received money to build a new radar which is scheduled to be built on the NE corner of Baffin Island in the Canadian Arctic. It will be their 5th radar.

No. Think of each integral as "stretching" to the next dimension. The path become a surface, etc.

I think there is a bit of difference in thinking here. Most people are thinking of a line as a discrete thing that iron filings or plasma or whatever exist on, making the "lines" real. That was what I was trying to show with my example. You have the correct thought that the "line" is just a mathematical construct - your integration shows this.

Exactly. The don't move, the simply align with the field. The direction the face is based on the direction of the field at the position of the filing itself. Think of each filing as a compass needle that points in the direction of the field at any point.

Unfortunately, iron filings themselves make for a difficult example other than showing the field. You are right, they become magnetized themselves via induction. The actual physics of the situation changes due to the small changes to the field. However, a sufficiently strong magnet will override any field cause by the filings themselves. Also, remember that the filings are each a "bar magnet" if you will and have a north and south pole which of course point toward each other (via attraction) which tends to cancel out many of the first order effects of the filings.

Your assumption of the filings moving and forming into lines however is incorrect. If you look closely, the filings don't all lie on a line, but simply close together. You're assumption of the effects that the filings have on each other is good though and this tends to cause the "gaps" you often see in pictures of magnets and filings (such as here.

You are also very correct in what you see is actually the OPPOSITE of what the "lines" themselves are doing. As the strength of the field increases, the "lines" get closer together while far from the magnet the lines are further apart. This is evident in the picture in the link above.

Also, you could set up an experiment where you had say some number of filings spread out nearly uniformly (as much as possible). When the magnet was applied, the filings would "spin" and align with the field (magnetic and the induced field). If you took a picture and did the experiment again, you would see a completely different "view" of the filings.

Good call... I'd give you an 'A' :)

Oops - I should have said that a field is a continuous function in 2 or 3 dimensions but a line is not... a line is continuous in 1 dimension (essentially a line is a 1-D field).

That is one way to think about it but that isn't entirely correct. A line is a discrete mathematical construct. A field is a continuous function but a "line" is not. Think about it this way: let's say you have a piece of paper and some "string". You place several piece of string on the paper. There is "space" in between the pieces of string. You then proceed to add pieces of string in between the others. You can continue to do this ad infinitum (assuming smaller and smaller pieces of string) but they will never match the piece of paper, i.e. the continuous field. They can approximate it but it will never be the same.

In this way, the magnetic field "line" is a mathematical construct used to determine topology. Electric field lines and gravity field lines are much the same thing. There is nothing wrong with saying "magnetic field line" save that iron filings or plasma or whatever is not on a line but in a field. They can be used to visualize the field, so to speak.

As a space physicist, I agree. Certainly we have seen an increase in the number of sunspots in the last month but most die out rapidly. However, other solar activity, such as corona holes (of which there are two) are becoming more common. The current set of holes should cause activity at the Earth on or about the 12th of July.

Magnetic field LINES are a mathematical construct. The magnetic field is real. Iron filings and plasma etc simply flow in the field. If there were lines, what would be between the lines? There could not be more lines. Therefore it is a continuous field. Iron filings simply represent that field.

Plasma on the other hand is an entirely different case because it is made up of charged particles. Plasma is therefore affected by the electric field as well as magnetic field. In fact, plasma flows with the rules of magnetohydrodynamics.

Magnetic field LINES are a mathematical construct. The magnetic field is real. Iron filings are just a way to visualize it. If there were "lines" then what would be in the space between them - couldn't be magnetic field lines... The magnetic field is continuous, therefore no lines.

I would wonder what the privacy commissioner would have to say about this comment?

Fortran is very important in the world of modelling and high speed computation. When I was an undergrad Fortran was taught for the physical sciences but the computer science dept refused to teach it so it was being taught by some geophysical modellers. I'm not sure that the university even offers Fortran anymore.

However, frustrated by that, the dept of physics and astronomy now has two courses in computational physics (both in Fortran) taught by modellers from the department. They deal with real world issues (well, real world modelling issues when applied to a spherical cow right?). Only one course is mandatory but both courses are very popular.

For myself, I use several modelling programs that are purely Fortran that I've had problems dealing with. I'm glad I did take a bit of Fortran though I am much more fluent in other languages these days. In fact my wife, in the private sector, has proprietary software that they use for modelling digital elevations and gravity fluctuation that is written purely in Fortran as well - simply for speed. Until someone invents a real quantum computer, I don't think Fortran in the physical sciences is going anywhere.