Flux Definition and 1000 Threads

Assume there is a boundary separates two medium with different heat conductivity [κ][/1] and [κ][/2]. In one medium, the temperature distribution is [T][/1](r,θ,φ) and on the other medium is [T][/2](r,θ,φ). What is the relationship between [T][/1] and [T][/2] ? Is it - [κ][/1]grad [T][/1]=-...

The correct answer is B, but I am not sure why. I have a few confusions regarding this problem. First of all, I had thought that we cannot use Gauss' Law to determine the flux through a SIDE of a cube since Gauss' Law only works for SURFACES. How can we determine how an electric field pierces a...

Let ##_\Omega \left\{ (x,y,z)\in R^3 : - \sqrt{3-y^2-z^2} \leq x \leq z+2 ,y^2+z^2 \leq 3 \right\} ## and consider the function ##f(x,y,z)=y^2x+z^2x## Represent the domain ##\Omega## compute the vector field ##F=\nabla f## compute the inward flux. So I've found that one is a cylinder of...

My idea is to evaluate it using gauss theorem/divergence theorem. so the divergence would be ## divF = (\cos (2x)2+2y+2-2z ( y+\cos (2x)+3) ) ## is it correct? In this way i'ma able to compute a triple integral on the volume given by the domain ## D = \left\{ (x, y, z) ∈ R^3 : x^2 + y^2 +...

What does this new find signify, i think we may be shortly due for something bad about to happen https://www.universetoday.com/144900/neutrinos-have-been-detected-with-such-high-energy-that-the-standard-model-cant-explain-them/https://arxiv.org/abs/2001.01737...

How and why does a changing magnetic flux induce an emf? Why doesn't a static one also produce one? How are the electric and magnetic forces related? Why do you move a wire through a magnetic field so that the wire, the motion, and the magnetic field are all mutually orthogonal in order to...

is it correct if i use Gauss divergence theorem, computing the divergence of the vector filed, that is : div F =2z then parametrising with cylindrical coordinates ##x=rcos\alpha## ##y=rsin\alpha## z=t 1≤r≤2 0≤##\theta##≤2π 0≤t≤4 ##\int_{0}^{2\pi} \int_{0}^{2} \int_{0}^{4} 2tr \, dt \, dr...

Given ##F (x, y, z) = (0, z, y)## and the surface ## \Sigma = (x,y,z)∈R^3 : x=2 y^2 z^2, 0≤y≤2, 0≤z≤1## i have parametrised as follows ##\begin{cases} x=2u^2v^2\\ y=u\\ z=v\\ \end{cases}## now I find the normal vector in the following way ##\begin{vmatrix} i & j & k \\ \frac {\partial x}...

I'm trying to understand the relationship between the "number" of field lines passing through a region and the magnetic force in this region.I understand that the drawings are of course conceptual: we cannot draw "all" the field lines (although can be visualized with iron fillings).Also the...

This is for an experiment to deflect a 28 SWG wire between two magnets, 3cm apart, by passing a current through it (example attached). The force on the wire is obviously F = BIL, but the wire will be passing at 1.5cm from each magnet so there will be some significant fall off of B and I can't...

q = 1.602e-19C mass_electron = 1.098e27 c = 3e8 Omega(Mag_flux_den) = 5GHz Lorentz factor = 100 synchrotron radiation at frequency v = 5GHz Mag_flux_den = (Omega(Mag_flux_den) * c * Mass_electron * Lorentz factor) / mass_electron Mag_flux_den = (5000 x 3e8 x 1.098e27 x 100 ) / 1.602e-19 =...

Inner conductor radius = 1cm outer conductor radius = 10cm region between conductors has conductivity = 0 & 𝜇r = 100 𝜇r = 1 for inner and outer conductor Io = 1A(-az) 𝑱(𝑟) = (10^4)(𝑒^-(r/a)^2)(az) Problem has cylindrical symmetry, use cylindrical coordinate system. Find the total current...

I wanted to check my answer because I'm getting two different answers with the use of the the Divergence theorem. For the left part of the equation, I converted it so that I can evaluate the integral in polar coordinates. \oint \oint (\overrightarrow{V}\cdot\hat{n}) dS = \oint \oint...

Is it the same as the plasma density ? Is it directly proportional to the plasma density ? Does this term only applies to electropositive plasma or applies to any plasma?

I have this problems I am trying to figure out: So I know that $$\int B\, dA = 0 = \phi_{total}$$ $$\phi_{total} = \phi_{bottom} + \phi_{top} + \phi_{side} = 0$$ $\phi_{side}$ must be equal to the other two fluxes, since they are both outwards: $$\phi_{side} = \phi_{bottom} + \phi_{top}$$...

I am trying to understand the stress-energy tensor. Say you have a gas of particles moving with random direction, but all with mass ##m## and velocity ##v## in a frame where the centre of mass is at rest. The contribution to the flux of x-momentum of a particle moving with ##\vec p = p \vec...

Since there is no charge inside the cone, the total flux through its surface is zero, hence Ø(lateral surface)+∅(base surface)=0. But ∅(base surface)=E.πR².cosΩ, because electric Field is homogenous. But by the figure, Ω is just arctg(h/R). So Ø(lateral surface)=-E.π.R².R/√(R²+h²). This is not...

This is an excerpt from a high school physics textbook. I don't understand the possible reason behind this statement. If we change something in the circuit say for example add a resistor , the current and hence the flux should change. Then why/how is this statement true?

I drew an illustration to make this easier: Point P is where I wish to find the magnetic flux density H. Given the Biot-Savart formula: $$d\textbf{H} = \frac{I}{4\pi}\frac{d\textbf{l}\times\textbf{R}}{R^2}$$ I can let $$d\textbf{l} = \hat{z}dz$$ and $$\hat{z}dz\times\textbf{R} =...

In Bransden textbook, it is stated that the probability current density is constant since we are dealing with 1-d stationary states. It gives probability flux outside the finite potential barrier which I verified to be constant with respect to x, but it doesn't provide the probability current...

The T^0i the components of the energy momentum tensor that correspond to mass flux and/or momentum density. If I wanted to get standard units of flux I would just multiply by c^2 correct? It is the ith component of momentum across the kth surface? I am thinking of an example in particular that...

Hi! My main problem is that I don't understand what the problem is telling me. What does it mean that the surface is a flast disc bounded by the circle? Is the Gauss surface the disc? Does that mean that inside the circle in the figure, there is a disc? Can you give me some guidance on how to...

Given that L is the luminosity of a single star and there are n stars evenly distributed throughout this thin spherical shell of radius r with thickness dr, what is the total intensity from this shell of stars? My calculations were as follows: Intensity is the power per unit area per steradian...

The flux applied to copper pipes and fittings before they are soldered together is said to suck the solder into the space between the fitting and the pipe. Empirically, the solder does flow into the narrow space. What physical phenomenon causes this? - an actual vacuum?

I am trying yo find the flux in a cell which is bounded by two concentric spheres and a cone. When I run the code I get a warning that no cross section tables are called for in this problem and a tally result of zero. The way I defined the surfaces and cells is below if anyone sees where I...

Homework Statement: Consider electron precipitating vertically into an auroral arc of area 1.0 km x 1200 km in the horizontal plane. The energy of the electrons is equal to 5 keV and the electron flux is 8.0 x 10^13 m^-2 s^-1. Determine the total particle energy into the arc, the total current...

I greatly appreciate this opportunity to submit a question. Is the thickness of a surface of any relevance while estimating the flux through it, as is mentioned in the following? Thankful for any advice.wirefree

Summary: Can a rotating AC Magnetic field induce movement in a static DC Magnetic flux? I'm designing a control panel, and the customer has asked us to reduce the EMC as much as possible; there are no drives, or other noise creating devices, just AC circuits. I thought a good starting point...

We can solve for the maximum 5 lux illumination distance with the above equation. E = 10.76*(35,000/d^2) d = 275 feet (approximately). However, the 5 lux illumination distance is not 275 feet. The 35,000 cd value is not an axial intensity value. It is at a point that is slightly down and to...

I tried finding the cone's Flux and from there i have no idea ,can anybody pls help me ? Thanks in Advance Regards Harish R

I don't know where to even begin?

The general interpretation of flux as I understand it (and please correct me if I'm wrong) is that it represents how much something is going through another (surface or volume (and perhaps lines?)), I'll quote Khanacademy : Considering that magnetism is a force, I very well understand that we...

I am checking the divergence theorem for the vector field: $$v = 9y\hat{i} + 9xy\hat{j} -6z\hat{k}$$ The region is inside the cylinder ##x^2 + y^2 = 4## and between ##z = 0## and ##z = x^2 + y^2## This is my set up for the integral of the derivative (##\nabla \cdot v##) over the region...

I will first calculate the magnetic flux of the coil in motion. $$\frac {d\phi}{dt} = -\frac {dB_{loop}}{dt}A = -\frac{d}{dt}(\frac{\mu_o}{4\pi}\frac {2\pi NR^2I}{(R^2+z^2)^{\frac{3}{2}}})A$$differentiating in terms of ##z##, we get $$\frac {d\phi}{dt} =(\frac{\mu_o}{4\pi}\frac {6\pi^2...

Homework Statement [/B] I’ve attached an image of the problem below. I need to use the diveragance theorem to find the flux through a cylinder. Vector field: F(x,y,z) = 4xi Height: 5 Radius: 3 Homework Equations By the DT, flux is equal to the triple integral of the divergence of the...

Assume such a situation, if I have a wire and some part of that wire passes through a hole in the core of an inductor or transformer or any other high magnetic field environment , are there ways to shield the wire, the part that intersects with the B field in order to prevent the field from...

Homework Statement A point charge q is placed inside a cube of side 2a. What will be the flux associated with the lower surface ABCD? Homework Equations I think I can apply Gauss Law here, but can't think of something connecting it with the lower surface. ∫B.dl = 1/ε° X Charge Enclosed The...

Homework Statement A charge q is placed at one corner of a cube. What is the value of the flux of the charge's electric field through one of its faces? Homework Equations The flux surface integral of an electric field is equal to the value of the charge enclosed divided by the epsilon_naught...

I have studied that mass transfer is of two types Molecular mass transfer(diffusion) Eddy diffusion then in later portion of the book I found that there is convective mass transfer too, I wanted to ask if both convective mass transfer and eddy diffusion are same ? I read this equation N_i =...

I'm new to ANSYS Maxwell and I'm trying to follow the inductance calculation example in the user's guide. The results for the inductance are pretty close but the value of flux are very low. What cause this? What should I do?

Homework Statement A coil has 460 turns and self-inductance 7.50 mH. The current in the coil varies with time according to i=(680mA)cos[πt/(0.0250s)]. What is the maximum average flux through each turn of the coil? Homework Equations ##\varepsilon_{ind} = N \frac{d\Phi}{dt} ...

Why is it that when integrating over all angles, integration is over the solid angle omega composed of theta and phi but the vector angle within flux, phi( r, E, omega), is resolved into the cartesian coordinates by cos(theta)sin(phi), sin(theta)sin(phi) and cos(phi) which is essentially the dot...

Hi, initially I have read that magnetic flux is conserved in iron core, also I know divergence of B is zero but this conservation implies that there is no flux at the interface of air and iron core surface. We still magnetic field even at the interface so there must be flux. Why do we exclude...

Homework Statement A 2cm x 3cm rectangle lies in the xy plane. What is the electric flux through the rectangle if Electric field= (100i +50k) N/C Homework Equations Φe=E⋅Acosθ (Electric Flux Equation) The Attempt at a Solution My question is to find the magnitude of the electric field we...

Homework Statement You have decided to use a CCD camera to check if a 16th magnitude quasar is variable. With your telescope/camera combination, you know that a star with a magnitude of 0 would deliver 1 × 109 photons/second to one pixel, so this allows you to work out the photons/second from...

Homework Statement Compute the flux of a vector field ##\vec{v}## through the unit sphere, where $$ \vec{v} = 3xy i + x z^2 j + y^3 k $$ Homework Equations Gauss Law: $$ \int (\nabla \cdot \vec{B}) dV = \int \vec{B} \cdot d\vec{a}$$ The Attempt at a Solution Ok so after applying Gauss Law...

Suppose I had cylindrically-symmetric rotating magnet surrounded by a plasma. I rotate it on its axis at a constant angular velocity, and so the electric field E produced is non-solenoidal and can be described as the negative gradient of some potential V(x,y,z). The electric field is induced...

Homework Statement A vector field is pointed along the z-axis, v → = a/(x^2 + y^2)z . (a) Find the flux of the vector field through a rectangle in the xy-plane between a < x < b and c < y < d . (b) Do the same through a rectangle in the yz-plane between a < z < b and c < y < d . (Leave your...

There is a solenoid of a certain radius, carrying a certain current. I draw an amperian loop of radius greater than the radius of the solenoid. If I calculate the total flux through this loop it should be, 1) Non zero for an ideal solenoid (where the field outside the core of the solenoid is...

Homework Statement A straight wire of length 0.20m moves at a steady speed of 3.0m/s at right angles to a magnetic filed of flux density 0.10T. Use Faraday's law to determine the e.m.f. induced across the ends of a wire. Homework Equations E= Nd Φ/dt but N=1 so E= dΦ/dt The Attempt at a...