# What is flux?

Celestiela
I'm totally confused as to what flux is... magnetically and electrically. MY professor was kinda talking it like it's a density of field lines, but then you start to read on about induction and other stuff, and flux doesn't make any sense anymore. If someone could help me out conceptually, that would be so cool. :!)

mathmike
flux is represented by the number of electric field lines penetrating some surface.

neurocomp2003
its the amount of substance crossinga barrier.

Celestiela
But arent there infinitely many field lines?

Delta
One thing not to be confused with is that Flux is not a couple of dotted lines that you see in the pics around magnets. But Flux actually surrounds the whole thing, the field lines are just a guide to show what direction the flux is going and what it generally looks like.

The best way I can describe it is that flux is like a magnetic current. EM circuits generate magnetic fields (measured in Tesla) which are full of flux. To quantify this flux we take an area of the field and multiply it by the field strength.

When you hold two opposing magnets close to each other you feel a force against you and that's flux.

In terms of induction, a current in a coil produces a field of flux. When this current changes, the flux changes in proportion. An adjacent wire will feel this flux and charges inside will move with the chaning flux causing a current in that wire.

In a way, but probably a bad example, its like if our eyes are subjected to changing intensities in light our pupils will change.

In E&M, Flux is defined with respects to the Electric or Magnetic field and a surface.

The flux of a field F through a surface S is

$$\iint_S \vec{F} \cdot \vec{da}$$

It is the surface integral of the dot product of the field and the local surface normal vector, taken over the entire surface.

I prefer not to think of it in terms of field lines, but rather, think of a fluid* flowing somewhere, and you have a surface immersed in the fluid. The flux is how much total fluid goes through the surface per unit time. So, a larger surface, or a faster-flowing stream, gives you a greater flux.

When thinking about field lines, you only look at a finite, 'representative' number of them. You're just drawing a picture, a conceptual model - your limitation is (quote David Griffiths) "your patience, and the sharpness of your pencil". The density of field lines represents the strength of the field locally - that's what the visualization is useful for. Near a point charge, there are lots of field lines coming together, so the E field is stronger.

*not a material fluid, the E field has point 'sources' and 'sinks'

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Jelfish
(prepare yourself for a horrible analogy)

Think of space as the ocean and the field lines as fish. Now, imagine there is one part of the ocean that has an abnormally large number of fish. Also, these fish come in many different lengths. Now say you're a fisherman and you want to catch some fish. Your salary, however, is dependent on the length of the fish you get, i.e. the longer the fish, the more money for which you can sell the fish. There's also another catch. The longer fish are a lot stronger and faster than the smaller ones, and so you can only allow so many to pass into your low-tech circular net at the same time or else your net will break or the fish will force the net out of your hand.

So now you have some calculating to do. You don't want to lose or break your net, but at the same time, you want to get as much as possible. Therefore, you must consider two things - the size of your net and the size/strength of the fish you're going to catch. If you're in an area of really small fish, you want to use a larger net. If you're in an area with large fish, you want to use a slightly smaller but stronger net.

Think about this relationship between netsize and fish size. You can sort of picture an inverse proportion between them. Think of flux as the proportionality constant between this relationship. It's the product of the opening size of your net and the strength/size of the fish. Alternatively, you can think of flux as the amount of money you'd make, since, in my made-up world, selling the large net's worth of small fish gets you the same amount of money as the small net's worth of large fish.

Now (the tricky part), try to apply this situation to electromagnetism. As you said, there are, theoretically, an infinite number of field lines. This is because it is assumed that these field lines affect all of space and therefore should exist everywhere. However, the strength of these field lines is not the same everywhere (This is the part that you have to convince yourself). Recall that the electric field of a point charge decreases by 1/(r^2). Flux is always calculated, as previous posters have said, as the product of the surface area and the perpendicular field that penetrates that surfaces. Think of the surface as the 'size of the net' and think of the perpendicular field as the fish that are swiming directly into the net.

Now, say you are trying to find the induced current on a loop of wire. It turns out that it is proportional to the magnetic flux through that loop. Think of the magnetic field as being the 'fish' and the loop of wire being the 'net.' To find the magnetic flux, you need the amound of field passing through the loop.

I hope that helps, though I completely understand if it doesn't.

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