Flux & Flux Density

Flux comes from the Latin word fluxus which means flow. There are two common uses for the term flux. In the transport phenomena, flux is defined as the rate of flow of a property per unit area. Flux as a mathematical concept also represents the surface integral of a vector field. Both definitions of flux are based heavily on mathematics and differential calculus.

In the transport phenomena there are eight different types of transport fluxes. The eight include: momentum flux, heat flus, diffusion flux, volumetric flux, mass flux, radioactive flux, energy flus and particle flux. Each of these fluxes are vectors at each point in space and have a definite magnitude and direction. For incompressible flows, the divergence of the volume flux is zero.

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The surface integral of flux is

 

Where

F is the vector field

dA is the vector area of the surface A

The surface normal is directed usually by the right-hand rule. Once can consider the flux the more fundamental quantity and call the vector field the flux density. Often a vector field is frawn by curves following the flow. The magnitude of the vector field is then the line density. The flux through a surface is the number of lines.

Solving a Diffusion Equation
The one-dimensional neutron diffusion equation with a plane source is [see the attachment for equation] where [attached] is the neutron flux, [attached] is the plane source at x = 0, and D and K^2 are constants. a) Solve this equation by applying the Fourier transform. b) Transform your solution back into the x-space.

X-Ray Tube Flux
Consider an x-ray tube in which electrons are accelerated by a constant high voltage of 250kV. If the electron beam current is 10 mA, calculate the x-ray energy flux (Energy fluence rate) at a distance of 1m from the tungsten anode target. Neglect absorption by the glass, and assume that the bremsstrahlung is emitted isotropical

Energy Fluence
The photon fluence rate is 10^7 photons mm^-2 sec^-1 for a beam of gamma rays. One fourth of the photons have energies of 100keV, one half have energies of 80 keV and the remaining quarter have energies of 20keV. What is the energy flux density (energy fluence rate) of the beam? If the photon photon flux density (fluence rate) i

China State in Flux
I need help on writing a response discussing a state (China) that has been “in flux” between a democracy and another form of goverment over the past 20-25 years (an example might be Russia’s struggle with establishing a democracy).

Gauss’ Theorem
If a vector field v is constant through space, use Gauss’ divergence theorem to show that the flux integral … must be zero, when taken over any closed surface S in three dimensions. Please see the attachment for the full problem.

Charge on concentric grounded spheres
Two conducting spheres are concentric, the inner sphere with radius a and the outer sphere with radius b. One sphere is grounded and the other is at potential V0. Find the charge on each when the grounded sphere is (a) the outer one and (b) the inner one.

Calculation of total flux linkage of a coil
** Please see attachment for the complete problem description ** The formula is: Lambda=NxPhi=N1phi1+N2phi2+N3phi3…etc. 16. Find the total flux linkage of the coil shown in Fig. 47 (please see the attached file) if each flux line represents 2 * 10^-7 Wb. 1) 28 * 10^-7 Wb-turns 2) 33 * 10^-7 Wb-turns 3) 38 * 10^-7 Wb-

Electric Field in a Tube
What is the electric field due to a long hollow copper tube carrying charge with density 15 Micro Coulombs per meter, at a point outside the tube 3.6 cm from its central axis and not near either end of the tube? What is the field at a point inside the tube?

Magnetic circuit model: A second winding is added
The core illustrated in Fig. 13.51(a) is 1 cm thick. All legs are 1 cm wide, except for the right-hand side vertical leg, which is 0.5cm wide. You may neglect nonuniformities in the flux distribution caused by turning corners. a) Determine the magnetic circuit model of this device, and label the values of all reluctances in

To determine the total magnetic flux through the plastic of a soda bottle
An open plastic soda bottle with an opening diameter of 2.4 cm is placed on a table. A uniform 1.55-T magnetic field directed upward and oriented 29 degrees from vertical encompasses the bottle. What is the total magnetic flux through the plastic of the soda bottle?

Magnetic field intensity at the centre of solenoid.
Calculate the magnetic field intensity in ampere-turns per meter, for each of the following solenoids: a. I= 40 mA, N= 500 turns, I = 0.2m b. I = 100 mA, N=1000 turns, I=0.5m c. I = 60mA, N=600 turns, I= 0.25m d. I=10mA, N= 300 turns, I = 0.075m Iron coil has field intensity of 50 A*t/m, if the relative perme

Rank surfaces in order of the electric flux through them
Each of the surfaces listed below is a flat plate iwth area vector A that lies in a region of uniform electric field E. Rank the surfaces in order of the electric flux through them, from most positive to most negative. Surface 1 A= (5.0 m^2)i – (4.0 m^2)j E= (3.0 N/C)i – (4.0 N/C)j Surface 2 A= (5.0 m^2)i – (4.0 m^2)

Magnitude of the magnetic flux through the top of a desk
At a certain location, the Earth’s magnetic field has a magnitude of 5.93E-5 T and points in a direction that is 70.0° below the horizontal. Calculate the magnitude of the magnetic flux through the top of a desk at this location that measures 109 cm by 60.0 cm. -Please explain and solve problem.

Electrons per Atom and Bohr Magnetons
The magnetization M of iron can contribute as much as 2 Tesla to B. If one electron contributes one Bohr magneton, how many electrons per atom on average can contribute to M? bohr magneton = 9.27 X 10^-24 J/T

Flux Through a Surface Due to Earth’s Magnetic Field
At a certain location, the Earth’s magnetic field has a magnitude of 5.93E-5 T and points in a direction that is 70.0° below the horizontal. Calculate the magnitude of the magnetic flux through the top of a desk at this location that measures 109 cm by 60.0 cm. Please explain and solve problem.

Electromagnetics: Magnetic Flux and Induced EMF
Which of the following statements are true about magnetic flux and induced EMF? 1) in order to make an induced EMF, the magnetic flux must be weak 2) in order to make an induced EMF, the magnetic flux must be static (steady) 3) the induced EMF has nothing to do with how fast the magnetic flux is changing through the

exact value flux integral
F ⃗=(18z+6y+cos^2 (x^2 )) i ⃗+(sin^2 (y)+5z) j ⃗+(e^(z^2 )+12y)k ⃗ Let C be the circle of radius 7 in the plane x + y + z = 24, centered at (8, 8, 8) and oriented counterclockwise when viewed from the origin. Find the exact value of c · d

Flux Integral of Surface Plane
Let S be the part of the surface z = 49 – (x2 + y2)2 above the xy-plane, oriented upward. Let D be the disk in the xy-plane given by x2 + y2 less than or equal to 7, oriented upward. F=yzi^+xzJ^+(-2+xy)k^ Compute the flux of F through D.’ Compute the flux of F through S.

Flux integral cylindrical radius
F=xi^+yj^+z^k and s is a closed cylinder of radius 2 centered on y axis with -3< y <3 and oriented outward

Insulating material bombarded with electrons – charge density
In pdf format, please provide the following, the derivations of formulae. I will draw all the sketches myself: When a block of insulating material such as Lucite is bombarded with electrons, the electrons penetrate into the material and remain trapped inside. In one particular instance a 0.1 microampere beam bombarded an

Accrued Accounts Payable and VAT Taxes
Can someone take a look at the below explanations and let me know if I need to change how it is worded? Please make any suggestions you deemed as necessary. Thanks. 1 – “Decrease In the accrued Accounts Payable (A/P) account is due to larger A/P accrual in December 2008 of $2.0M vs. A/P accrual in May 2009 of $1.8M; larger

Electrostatics: Charge density in a coaxial cable.
We have a long coaxial cable with an inner solid wire of radius a and outer metal shell of radius b. On the inner wire, the volume charge density is given by ks2 . On the outer shell, the linear charge density (along the axis) is given by &#955;. (a) Draw a picture that illustrates this arrangement. (b) What is the lin

Flux of a Vector Field
Please note this: In my textbook theta is angle from Z-axis to the vector-r Phi is the angle from the x-axis to the vector projection on the x-y plane Compute the total flux…of the vector field…out through sphere

Electrostatics: Electric flux through a rectangular sheet.
A flat sheet is in the shape of a rectangle with sides of lengths 0.400 m and 0.600 m . The sheet is immersed in a uniform electric field of magnitude 74.5 N/C that is directed at 20 degrees from the plane of the sheet (see the attachment). Find the magnitude of the electric flux through the sheet.

Strategic Global Logistics Paper: compare factors that impact transportation needs
Select an organization and prepare a paper addressing the following items: a. Identify and compare at least four to five factors (cost, shelf life, weather, etc.) that impact transportation needs. b. Determine appropriate logistics methods in various scenarios (local, out-of-state, regional, coast-to-coast, and global)

The outward flux
See attached page for problem Let S be the surface of the solid hemisphere bounded by (see attached)

Counterclockwise circulation and outward flux
Use Green’s Theorem to find the counterclockwise circulation and outward flux for the vector field F(x,y)= xyi + x^2j and the curve C, where C is the boundary of the region enclosed by the parabola y=x^2 and y=x

Extraction and purification of iron
Describe in detail the extraction and purification of iron.

Flux of a Field : Let S be the surface that is bounded on the left by the hemisphere…
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