- #1
Rasalhague
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Am I right in thinking that flux can mean either a surface integral of the dot product of a vector field with a unit vector perpendicular to a given surface (the total flux through a surface of area A):
[tex]\int \mathbf{F} \cdot \hat{\mathbf{N}} dA,[/tex]
(e.g. electric flux, magnetic flux), or such a total divided by the area of the surface:
[tex]\frac{\int \mathbf{F} \cdot \hat{\mathbf{N}} dA}{A},[/tex]
(e.g. volumetric flux)? The latter kind of flux seems sometimes to be expressed as a vector quantity, as in the Poynting vector and heat flux (also called heat flux density), although some sources only call the magnitude of the Poynting vector energy flux. Is this just a matter of convention or convenience? What happens if the surface isn't flat; which direction does the vector point? Have I even got the right formula for defining it? Is total flux ever expressed as a vector?
I gather that total flux, in the relavant contexts, may be called mass flow rate and volumetric flow rate, while the per-area flux is called mass flux and volumetric flux. Are these terms limited to certain instances of flux in the broader sense? What are electric and magnetic flow rate (are they synonymous with electric and magnetic flux, as normally defined, or do they refer to something else)?
I read in Wikipedia that energy flux can refer to either kind of flux, total or per-unit-area, the latter sometimes being called flux density, and I've seen the Poynting vector called an energy flux density vector. Does the term "flux density" applied to the magnetic B field have the same meaning as "flux density" when it's the per-unit-area kind of energy flux, or is it a flux density in the sense that Davis and Snider use the term in Introduction to Vector Analysis, § 3.7, where they define flux density of the flux
[tex]\mathbf{F} \cdot \hat{\mathbf{N}} ds[/tex]
as the function F, or does flux density have some other sense when applied to the magnetic B field?
What is flow rate density? Why is density used for a "per unit area" quantity, as opposed to pressure; is it just a linguistic quirk/convention?
Are there general, unambiguous terms for these concepts? Are there other uses of the words flux and flux density, etc. in physics that I haven't covered.
[tex]\int \mathbf{F} \cdot \hat{\mathbf{N}} dA,[/tex]
(e.g. electric flux, magnetic flux), or such a total divided by the area of the surface:
[tex]\frac{\int \mathbf{F} \cdot \hat{\mathbf{N}} dA}{A},[/tex]
(e.g. volumetric flux)? The latter kind of flux seems sometimes to be expressed as a vector quantity, as in the Poynting vector and heat flux (also called heat flux density), although some sources only call the magnitude of the Poynting vector energy flux. Is this just a matter of convention or convenience? What happens if the surface isn't flat; which direction does the vector point? Have I even got the right formula for defining it? Is total flux ever expressed as a vector?
I gather that total flux, in the relavant contexts, may be called mass flow rate and volumetric flow rate, while the per-area flux is called mass flux and volumetric flux. Are these terms limited to certain instances of flux in the broader sense? What are electric and magnetic flow rate (are they synonymous with electric and magnetic flux, as normally defined, or do they refer to something else)?
I read in Wikipedia that energy flux can refer to either kind of flux, total or per-unit-area, the latter sometimes being called flux density, and I've seen the Poynting vector called an energy flux density vector. Does the term "flux density" applied to the magnetic B field have the same meaning as "flux density" when it's the per-unit-area kind of energy flux, or is it a flux density in the sense that Davis and Snider use the term in Introduction to Vector Analysis, § 3.7, where they define flux density of the flux
[tex]\mathbf{F} \cdot \hat{\mathbf{N}} ds[/tex]
as the function F, or does flux density have some other sense when applied to the magnetic B field?
What is flow rate density? Why is density used for a "per unit area" quantity, as opposed to pressure; is it just a linguistic quirk/convention?
Are there general, unambiguous terms for these concepts? Are there other uses of the words flux and flux density, etc. in physics that I haven't covered.