- #1
Rasalhague
- 1,387
- 2
Here's what I understand by flux:
[tex]\int \textbf{F} \cdot \textup{d}\textbf{A},[/tex]
the surface integral of a vector field. I gather the vector field that's integrated to give a flux is called the flux density (examples: the magnetic B field for magnetic flux, the Poynting vector for electromagnetic energy flux, mass "flow-rate" density for mass flux, and j charge density for current). I gather that the flux density through a surface is a scalar, the dot product of flux density (the vector) with a unit vector normal to the surface. For this, we need to specify an orientation of a surface at the relevant point, but not the size or shape of the surface. A related concept, when some surface is fully specified, is average flux density:
[tex]\frac{\int \textbf{F} \cdot \textup{d}\textbf{A}}{A}.[/tex]
Exceptions: the flux density of electric flux is called the electric field, E, which differs from the related vector quantity called electric flux density, also called the electric displacement field, D. I don't know why, but then I don't know much about these concepts.
I also gather that the term "flux" is often loosely used in place of "flux density" (presumably in any of the senses of that latter). Are the 2nd, 3rd and 4th components of the top row of the stress-energy tensor [ http://en.wikipedia.org/wiki/Stress-energy_tensor ], here called "energy flux", actually energy flux density, the same kind of quantity as the Poynting vector? And does "energy density" here mean the limit of average energy per unit volume at a point as the volume goes to zero?
[tex]\frac{\mathrm{d} E}{\mathrm{d} V}[/tex]
Given the analogy between mass flux and current, is current synonymous with "charge flux", if that term is used?
[tex]\int \textbf{F} \cdot \textup{d}\textbf{A},[/tex]
the surface integral of a vector field. I gather the vector field that's integrated to give a flux is called the flux density (examples: the magnetic B field for magnetic flux, the Poynting vector for electromagnetic energy flux, mass "flow-rate" density for mass flux, and j charge density for current). I gather that the flux density through a surface is a scalar, the dot product of flux density (the vector) with a unit vector normal to the surface. For this, we need to specify an orientation of a surface at the relevant point, but not the size or shape of the surface. A related concept, when some surface is fully specified, is average flux density:
[tex]\frac{\int \textbf{F} \cdot \textup{d}\textbf{A}}{A}.[/tex]
Exceptions: the flux density of electric flux is called the electric field, E, which differs from the related vector quantity called electric flux density, also called the electric displacement field, D. I don't know why, but then I don't know much about these concepts.
I also gather that the term "flux" is often loosely used in place of "flux density" (presumably in any of the senses of that latter). Are the 2nd, 3rd and 4th components of the top row of the stress-energy tensor [ http://en.wikipedia.org/wiki/Stress-energy_tensor ], here called "energy flux", actually energy flux density, the same kind of quantity as the Poynting vector? And does "energy density" here mean the limit of average energy per unit volume at a point as the volume goes to zero?
[tex]\frac{\mathrm{d} E}{\mathrm{d} V}[/tex]
Given the analogy between mass flux and current, is current synonymous with "charge flux", if that term is used?
Last edited: