In chemical engineering, we deal with molar fluxes and I am very sure molar flux is not a vector, it is simply a scalar. molar flux cannot be negative because you cannot have - 5.0 moles of something flowing but I think you'll have to verify for other cases like magnetic flux and electrical fluxes
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
Resultant vector or effective vector
Vector spaces can be formed of vector subspaces.
A null vector has no magnitude, a negative vector does have a magnitude but it is in the direction opposite to that of the reference vector.
Scalar
The poynting vector is that one which represents the directional energy flux density of the electromagnetic field.
Magnetic flux through a surface is maximum when the direction of the magnetic field is in the same direction as the normal vector of the surface. In other words, the magnetic flux is maximum when the magnetic field is perpendicular to the surface area. That's why φ=BAcosθ, where θ is the angle between the direction of the magnetic field and the normal vector of the surface area. When the magnetic field is exactly the same direction as the normal vector (aka the magnetic field is perpendicular to the surface), θ=0 and cosθ = 1, its maximum value. The closer θ is to 90 degrees (ie. the more parallel the direction of the magnetic field is to the surface area, or the less parallel the magnetic field is to the surfaces normal vector), the smaller cosθ is, and thus flux will decrease accordingly.
The applications are in transport phenomena, in determining the direction of flow in momentum transport, heat transfer, and mass flux.
A flux integral is the summation of the component of a vector field perpendicular to differential surface areas (or in the direction of their normal vectors) over the entire surface. In other words, the flux of a vector field across a surface is the surface integral vector field in the direction of the normal component of the surface.INT INTS[(F*n)dS]INT INT is the double integral operatorS is the surface domain being integrated overF is a vector field* is the dot productn is the normal component to the surfacedS is the differential surface area.Flux integrals are very useful in physics. Two of Maxwell's equations involve flux integrals:INT INTS[(B*n)dS] = 0This equation states that the magnetic flux over a closed surface is always equal to zero. This equation reflects the fact that magnetic monopoles do not exist.INT INTS[(E*n)dS] = Q/EThis equation states that the electric flux through a closed surface is proportional to the total charge enclosed within that surface (1/E is the proportionality constant). These equations played important roles in the discovery of electromagnetic radiation.also the Flux of a velocity field through a surface indicates the flow rate across that surface.
Change in magnetic flux.iechange in magnetic field (B).change in the area vector/ area of magnetic field under the closed circuit (A).The angle between area vector and magnetic field .......xomagnetic flux = cosxo . A . B
Dennis C. Jespersen has written: 'A time-accurate multiple-grid algorithm' -- subject(s): Multigrid algorithms 'Flux vector splitting and approximate Newton methods' -- subject(s): Euler equations of motion, Flux splitting
Cristian Anghel has written: 'Sensorless flux vector control for a permanent magnet synchronous machine with cylindrical rotor under severe starting conditions'
i) leakage flux is those flux which goes through the air and linkage flux is those flux whose go through the cell. ii)leakage flux is the loss at flux but linkage flu is warning flux. iii)leakage flux is cause of eddy current loss and linkage flux is case of copper loss.
The Ratio of the total flux ( flux in iron path) to the useful flux (flux in air gap)
when a current flow through the coil then flux produced around the coil . if the flux linked same produced coil only then the flux is said to be leakage flux. flux produced by one coil ,but linked with another coil then the flu is said to be mutual flux.
when a current flow through the coil then flux produced around the coil . if the flux linked same produced coil only then the flux is said to be leakage flux. flux produced by one coil ,but linked with another coil then the flu is said to be mutual flux.