Flux is a single unit, measured in Webers, that means the amount of
magnetic field lines that pass perpendicularly through a plane area.
Each of these factors are important so I'll expand on each one.
The field lines are just imaginary lines, but when drawing or discussing
magnets, it has become convenient to draw numerous lines in a path around
the magnet. If nothing else is nearby, the lines loop through the air from
the N pole to the S pole and finish the circuit inside the magnet material
going from the S pole to the N. If you wanted to compare two magnets but
one was stronger, you could illustrate this by drawing more lines, more
closely packed together, in the stronger magnet. This is what is done, in
fact. Usually the lines are arbitrary, but a physicist would consider it
important to space them apart properly, and to draw them travelling in the
correct paths. After that, using 10 lines per centimeter or 20 lines per cm
is really just a matter of convenience in the drawing - don't want to make a
cluttered drawing.
![What is Flux?](https://www.fieldlines.com/index.php?PHPSESSID=f10c12f784cf32b85c67fe7c30303eb4&action=dlattach;topic=143565.0;attach=515;image)
Now, about the plane area. You can keep it simple and only worry about the
coil of wire, but flux is important in various things such as attractive
force as well as current induction. That plane can just be some rectangle
"floating in space" and the magnetic field lines just pass through it. This
picture gets you away from what you are doing with the magnet, and creates a
picture of what is "mathematically" important instead. So if we have a
small rectangle hovering just past the N pole end of a bar magnet, then
there definitely will be some field lines passing through it. If we then
make the small rectangle a bit larger, it will probably pick up a few more
of the lines emanating out the end of the magnet. At some point, though,
the rectangle gets larger than the end of the magnet itself, so there are no
more lines to capture. All the lines emitted from the end of a 2 cm
diameter magnet come from that 2cm diameter face, hence, a 2cm circle is all
you need to catch them. A 3cm circle will catch no more, while a 1 cm
circle will catch only a few inside, and most will pass around it.
![What is Flux?](https://www.fieldlines.com/index.php?PHPSESSID=f10c12f784cf32b85c67fe7c30303eb4&action=dlattach;topic=143565.0;attach=516;image)
Now to take apart the word "perpendicular" that I used before. Each field
line coming out then end of a magnet curves away and loops back to the other
end of the magnet. Once it starts curving, then it's not pointed in the
same direction as the others. It also isn't pointed straight through our
circle any more, either. So this is a hindrance because only the part of
the line that is perpendicular to the plane area contributes to the flux.
Any part of the line that passes through the plane at an oblique angle makes
no difference. This may hearken back to your high school days (secondary
school, finishing school, whatever you blokes call it?) where one of your
math topics was vectors and finding the X component and Y component. Here
is a case were it matters. When the field line's X component (perpendicular
to the plane) is large, then the line contributes a significantly to the
flux, but when it passes through the plane at a shallow angle, only its Y
component is large, so the field line adds little flux.
![What is Flux?](https://www.fieldlines.com/index.php?PHPSESSID=f10c12f784cf32b85c67fe7c30303eb4&action=dlattach;topic=143565.0;attach=517;image)
The last step to take is to look at the case of holding up a really large rectangle
at the end of the bar magnet. Near the end of the N pole those lines go
through the plane straight and true... lots of flux... then start curving back
the way they do, and pass through the rectangle yet again. This is an awful
situation because this field line has cancelled itself out! No flux is gained at all.
There, the general principles. Applying it to a home-built electrical generator with permanent magnets should be easier for some. If others want more detail, nothing's stopping me from adding a second part later.
PS A suggestion about how to use the "FAQ" section.
clutter: comments and corrections invariably make the information in a FAQ better, but at the same time it makes it difficult for the uninitiated to find what they want. I suggest that we should feel free to comment, but if the correction or addition is put into the basic text, then the posting may be deleted. This process will incorporate improvements without clutter. An alternative to posting a comment is to sent a private message. If you click on my name "sparweb" you will see my profile, and you can send a private message with your correction there.
editing: the moderator will edit everything in the FAQ necessary to keep it clear and concise. The purpose is for teaching + learning, not a permanent record of one's latest exploits.