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## what is flux...?? is it a scalar or a vector and difference bet flux and flux density

i have read the articles where the flux (either in case of electric flux or magnetic )is described as the no of lines passing through a surface area ( open in case of magnetic characterized by boundary and closed in case of electric flux density) or considered as an component of electric field or mag. field through that surface..
below is exact context:-
 The magnetic flux through some surface, in this simplified picture, is proportional to the number of field lines passing through that surface (in some contexts, the flux may be defined to be precisely the number of field lines passing through that surface; although technically misleading, this distinction is not important). Note that the magnetic flux is the net number of field lines passing through that surface; that is, the number passing through in one direction minus the number passing through in the other direction (see below for deciding in which direction the field lines carry a positive sign and in which they carry a negative sign). In more advanced physics, the field line analogy is dropped and the magnetic flux is properly defined as the component of the magnetic field passing through a surface
from:- http://en.wikipedia.org/wiki/Magnetic_flux
but rather my textbook defines that it is convenient to replace sometimes the magnetic or electric field lines with flux lines..!!
FLUX LINES...: if its a scalar then how could we associate lines with it i mean we are here concerned with no of lines which is absolutely a scalar..
and further there was a post here about differences bet flux and flux density
and it was made clear that:-
 Magnetic flux, Φ, is a scalar, measured in webers (or volt-seconds), and is a total amount measured across a surface (ie, you don't have flux at a point). Magnetic flux density, B, is a vector, measured in webers per square metre (or teslas), and exists at each point. The flux across a surface S is the integral of the magnetic flux density over that surface: Φ = ∫∫S B.dS (and is zero for a closed surface) Magnetic flux density is what physicists more commonly call the magnetic field. It is a density per area, rather than the usual density per volume.
what i am here concerned about is that magnetic flux density is commonly called as mag field but if its so then why do we have the relation D=εE
where D is flux density and E is the electric field ..!!
further my textbook (sorry i can't show the diagram) gives that convention of magnetic flux lines across the n conductors and i can barely see the difference bet flux and field lines..
and to further confuse there is a point in case of parallel capacitors that aD=q
or area times flux density=charge ( the reason it is because it is parallel plates..)
this is all really confusing me a lot sometimes it says it is a scalar but at same time it gives me flux lines and also sometimes give me a hint that flux density and field intensity are same but then there exists a relation bet two..
what it is.....??
PS: and yes the textbook i have mentioned here is : network analysis by M.E VANVALKENBURG..!!

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shivaniits,

Your post is long, but I'll take a stab at addressing at least part of it. I have no idea what "flux lines" are, other than another (very poor) name for "field lines." The fields of classical electromagnetism are vector fields: mathematical functions that assign a vector to every point in space. As a result, they can be depicted by drawing arrows at each point in space (with a chosen sampling interval) to indicate the magnitude and direction of the field at that point. An alternate way to depict them, however, is to join up the arrows to form smooth, continuous curves called "field lines" that indicate the overall structure of the field. Information about the strength is not lost, because for a consistent choice of field line density (i.e. how many of them you draw for a charge of a given strength) the strength of the field is determined by how close together or far apart the field lines are. Imagine field lines radiating outward from a point charge: the field is stronger closer to the charge where the lines are denser and weaker farther away where they are more sparse. However, the flux through a closed surface around that charge, which is represented by the total number of field lines passing through it, is independent of the distance to that surface. This makes sense, because although the field strength diminishes as 1/r^2, the area of the surface increases as r^2, and the flux, which depends on the product of these two, is therefore constant. If you have a chance, you should check out section 2.2.1 in Introduction to Electrodynamics by David J. Griffiths, where he explains this better (pp. 65-67 in the third edition).

As far as "flux density" goes, its important to keep in mind that these are names, and the choice of names is sometimes arbitrary or historical. Just because the name has the word "flux" in it doesn't mean it is supposed to be the same type of quantity as the "flux" that you know of, that is defined in terms of a surface integral. Words are just words, and this wouldn't be the first instance of the same word being used in two different ways in physics (not by a long shot). After all, "flux" is just Latin for "flow." In any case, the two quantities are not of the same type. The "flux" of the electric field and the "flux" of the magnetic field, (##\Phi_E## and ##\Phi_B##) are scalars, whereas the quantity that some people refer to as the "magnetic flux density" B is unquestionably a vector. As I stated before, in terms of mathematical definition, the fields of electromagnetism (E, B, D, H, take your pick) are all vector fields. EDIT: I do see now from you original post that some sources justify the use of the term "flux density" for B, by noting that when you integrate it over an area, you get the magnetic flux. Fair enough.

For what it's worth, Griffiths balks at the choice of "magnetic flux density" as a name for B

 Quote by David J. Griffiths in Introduction to Electrodynamics Many authors call H, not B, the "magnetic field." Then they have to invent a new word for B: the "flux density," or "magnetic induction" (an absurd choice, since that term already has at least two other meanings in electrodynamics). Anyway, B is indisputably the fundamental quantity, so I shall continue to call it the "magnetic field," as everyone does in the spoken language. H has no sensible name: just call it "H."4 ------------- 4For those who disagree, I quote A. Sommerfield's Electrodynamics (New York: Academic Press, 1952), p.45: "The unhappy term 'magnetic field' for H should be avoided as far as possible. It seems to us that this term has led into error none less than Maxwell himself..."

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 Quote by cepheid EDIT: I do see now from you original post that some sources justify the use of the term "flux density" for B, by noting that when you integrate it over an area, you get the magnetic flux. Fair enough.
I'm not an EM guy, but you might find it easier to understand the words in for something like heat flow.

"Flux" is the total amount of heat flowing through a surface (measured as heat energy / second, i.e. power in watts)

"Flux density" is the flux per unit area, or sometimes the amount of heat generated per unit volume (for example heating something in a microwave oven, or heat generated by nuclear reactions).

FWIW, temperature is a scalar field (which is simpler to visualize than the vector fields in EM) and the direction of the flux is therefore the gradient of the temperature field. If you visualize a temperature distribution on a plane by drawing a contour map, the flux direction is at right angles to the temperature contour lines, and the magnitude of the flux density is higher where the temperature contours are closer together.

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## what is flux...?? is it a scalar or a vector and difference bet flux and flux density

In chemical and mechanical engineering, heat flux is always heat flow per unit area. The heat flux vector is equal to (minus) the thermal conductivity times the gradient in temperature.
 I am only an engineer, just happen to come to Classical Physics to ask a question of my own and see this post. This is my understanding: Magnetic flux density $\vec B$ is definitely a vector function where $$\nabla \cdot \vec B\;=\;0\;\hbox { and }\; \nabla \times \vec B \;=\; \mu\vec J\;+\;\frac{\partial\vec D}{\partial t}$$ But $\Phi$ is scalar where: $$\Phi\;=\;\oint_s \vec B\cdot d\vec s$$ In words, B is line density and has direction. The total B flux line that cross an area gives you the TOTAL ( scalar) flux through the area as the equation of $\Phi$ indicates.

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i totally consider the fact that electric field lines are merely (rather continuous) the tangential representations of force acting on unit charge at that point which is definitely a vector and flux measures the flow of electric field lines through a particular defined surface δs and that is somewhat similar to heat flow or amount of heat flow through a well defined surface hence scalar rather the flux density is somewhat we define at particular point just considering the temperature gradient at point which has a direction indicating heat flow at a pt hence becomes vector..but the thing that still confusing is :-
 in case of parallel plate capacitor which i have considered here the Da=q where D : flux density a: surface area q: total charge on one plate and we also know that surface charge density is defined as : charge density is a measure of electric charge per unit volume of space, in one, two or three dimensions. More specifically: the linear, surface, or volume charge density is the amount of electric charge per unit length, surface area, or volume, respectively. The respective SI units are C·m−1, C·m−2 or C·m−3 from: http://en.wikipedia.org/wiki/Charge_density so here in case of parallel plate capacitor we have charge density σ=q/a ( surface charge density charge per unit area) and we also have the relation bet flux density D with E electric field intensity D=εE and E=σ/ε ( one can find this from gauss law for parallel plate capacitors) so both D and σ are here equal and but we know that charge density is definitely NOT a vector but flux density is a vector so both being equal in magnitude one has defined as scalar and other as vector..??