Flux Definition and 1000 Threads

I have tried to understand the solution given in the book which is as pasted below. The solution uses Gauss's Law but makes no mention of which Gaussian surface is used. The diagram that I have used to understand this problem is also given at the end. From the diagram, faces OADG, OABE and OEFG...

I noticed that in some textbooks (Physics - Tipler) the electric flux formula is different than in other textbooks (Engineering Electromagnetics -W. Hayt) Which one should we use?

I have attached the work to this problem and although it has different parameters than what I have listed in my post the basis to solving the problem is the same. I am confused on why this rectangle in this problem is considered to b in the j unit vector direction. Is it because its face will...

Phi= int(E.da) through a surface S is a measure of “number of field lines” passing through S. I put this in quotes because of course we can only draw a representative sample of field lines. The total number would be infinite. But for a given sampling rate the flux is proportional to the number...

In the 7th edition of the book "Elements of Electromagnetics by Matthew N. O. Sadiku" On page 190 the author goes on to say: "We now consider the case in which the dielectric region contains free charge. If ##\rho_v## is the volume density of free charge, the total volume charge density...

Phi = int of (3xi^ + 4j^).vector dA = 3 int of(xdA) Now we put x= 3 and we get at last 36 N m^2/C. I am getting confused why E is a fuction of x. How can that be? How can we represent the E and position x on the same coordinate system. Is it right ? Because we know distance is inversely...

When I look at this question, I can see two possible values of electric flux depending on how I take the normal area vector for either ends ##A \text{ and } A^{'}##. What is wrong with my logic below where I am ending up with two possible answers? The book mentions that only ##2E\Delta{S}## is...

Gauss law relates between E at some point on guassian surface with the net charge enclosed by that surface. Using gauss law is like being able to tell what (ie charge)is inside a gift box by just looking at the wrapper(electric field). There are two types of problem. Sometimes we know the charge...

I am sure axial are used in wind turbines so i will use it as my example. Say you are using the wind turbine to generate power but its getting to windy and you want to slow down the turbine to bring it to a stop. What i want to know is ... If you can cut off the power that's been generated...

I think Flux density is flux/Volume. Or is it flux/ Area Please be kind to help

I don't understand the exact meaning of flux. Please be kind to help.

I am trying to see if Vector fields(I am thinking of electric and magnetic fields) without sources(divergence less) can be represented by a pair of functions f and g such that the level surfaces of the functions represent flux lines. I am trying to solve this problem in ## R^3 ## with a...

Three phase squirrel cage induction motor with given parameters (stator winding connected in delta) nominal power: Pn=22.4kW nominal stator voltage: Vsn=230V nominal stator current: Isn=39.5A nominal stator frequency: fsn=60Hz nominal speed: nn=1168min−1 number of pole pairs: 3 stator...

Summary:: Is the magnetic flux density B constant? Is the magnetic flux constant? I am working on a project design for Uni and I am stuck. In a magnetic circuit is either the magnetic flux or the magnetic flux density B constant? This magnetic circuit has all different cross section areas and...

Hello I've made a small program that does FFT, Fast Fourier Transform on a signal from radio receiver (RTL SDR), and parabolic antenna. Of course, the output is amplitude depending on frequency. I want to use it to detect and measure 1420MHz radiation from space. But I'm not sure on what's the...

taking origin at the centre of the square. ##d\phi = \vec E.\vec{da}## $$d\phi = \frac {kqa}{(x^2 + y^2 + a^2)^{3/2}} da$$ $$\phi = \int_{-a/2}^{a/2}\int_{-a/2}^{a/2}\frac{kqa}{(x^2+y^2+a^2)^{3/2}}(dx)(dy)$$ on evaluating this double integral i get $$\phi = (q/\pi{\varepsilon}_0...

I was reading about high temperature superconductors expelling magnetic fields (Meisner effect). I was curious if this only works with permanent magnets or is there similar effects with electromagnets. I assume since the magnetic waves would be similar there would be a similar reaction, but...

I'm trying to plot the solar spectrum (Wavelength versus Flux) from a table of values I'm given. I'm given 3 columns; Solar Flux Arcturus Flux Wavelength Plotting Solar Flux versus Wavelength gives me a graph (below) that is very difficult to resolve. There are 21,000 data points as well. If...

What is Flux Throughput? Explain how there can be a flux throughput advantage in using a coude spectrograph compared to a Cassegrain spectrograph? I'm confused on what this actually means when comparing the two. Is it asking what are the seeing advantages in terms of resolving powers of a...

I have solved the first 2 parts. For the 3rd part, I have obtained the equation: T(x) - T0 = (T1 - T0)e^(-Φx/fc), where f = fm in the question. How do I obtain that expression for H? Thank you!

I've been told that if you drop a magnet through a coil the induced emf and flux graphs would look like this: I understand that when the bar magnet is in the middle of the coil the emf induced is zero as flux change in top and bottom is in opposite directions but why is effective flux maximum...

Ok so here is something that made me scratch my head and I still can't come to a final conclusion. The basic idea is seemingly simple. You have permanent magnets attached to a core, the field lines close on both magnets through the core, so far so good. but the core also has electromagnets , put...

I calculated in this way as attached and got the correct answer. However I still wonder why the magnetic flux is the same in both coils, or this presumption is not right.

Hi everyone, i'm very new to the forum so i hope I've used the correct form to write my question. Anyway, i need some help to evaluate the result of my last analysis: I'm studying the flux flowing inside an ICE aspiration manifold in a very simplified way (1D flux, ideal gas, compressible...

Hello everybody To calculate the flux for the electric field I need the gauss law. There are two formula one with the integration over some area and the other is Q/e0. When do I have to use which one?

So I'm confused what the Saturation Flux Density is referring to. Defintion says it is when you no longer get an increase in H-field when increasing external B-field. So, does the satuation flux mean the core can only create fields UP TO that saturation flux, or that it can make a stronger...

I am interested in energy flux density from the Moon at Earth’s surface, specifically in infrared (albeit most of it comes in infrared anyway). Physics.SX (boyfarrell) gives an estimate 89 mW/m². I doubt it for several reasons. 400 K (as effective mean) on Moon seems to be unrealistically hot...

Hi everyone, I have a question about Maxwell's laws. According to Maxwell the magnetic flux of a magnetic field through a close surface is 0. But his third law says the circuitation of an electric field depends from magnetic flux variation. I can't understand how this can be possible since...

I know the answer is ##ka^3/2##. I got ##ka^2## and I don't know how to get the right answer. I saw an explanation using integrals, but my class is algebra-based. My attempt: ##Flux=ABcos\theta##. I figure ##cos\theta## is 1 becuase the angle between the magnetic field and the normal to the...

This is supposed to be very basic, where the loop is held there is a declining magnetic field in direction (-z), therefore the current is supposed to be clockwise. However in the answers it is said the the current is anti clockwise. That doesn't make sense to me. Is there a mistake in the answers?

Hello all, Apologies if this has already been asked before, but I tried researching this question for a while with no results. I was reading Grainger's Power System Analysis' derivation of the inductance of a single wire and got confused by his definition of magnetic flux linkage. He seems to...

I don't really know how to find it mathematically as I am really confused in finding the normal vector and finding the electric field as well. pls help

##4\pi\mathcal L = -\mathcal e \frac{\partial A_i }{\partial t} - \phi\mathcal E^i{}_{,i} -\frac{1}{2}N\gamma^{\frac{1}{2}}g_{ij}(\mathcal E^i \mathcal E^j +\mathcal B^i\mathcal B^j) +N^i [ijk]\mathcal E^i\mathcal B^j## MTW (21.100) I'm trying to produce the result required by the problem...

I have these equations in my book, but I don't know how I can use them in this problem Electric field of a plane has surface electric density σ: E = σ/2εε₀ Ostrogradski - Gauss theorem: Φ₀ = integral DdS Can someone help me :((

Can anyone explain the above answer to me? What does the "change in area" mean?

Question 1; a) P=E/t E=5.796*10^7 J energy produced per day during the summer However, I am not certain how to calculate the time period, since although this concerns the energy produced per day, the sun does not shine for the entire duration of this 24 hour period. Also, I am unsure of the...

I have been reading Griffith's Introduction to Electodynamics and i am currently at the chapter about magnetostatics. There is an example about a long solenoid with n units per length and radius R that shows a way of finding the magnetic vector potential. The magnetic field inside the solenoid...

##\vec F= 2x^2y \hat i - y^2 \hat j + 4xz^2 \hat k ## ## \Rightarrow \vec \nabla \cdot \vec F= 4xy-2y+8xz## Let's shift to a rotated cylindrical system with axis on x axis: ##x \to h, y \to \rho cos \phi, z \to \rho sin \phi ## Then our flux, as given by the Divergence theorem is the volume...

Hi! I was wondering why even a real transformer has a very low leakage flux, what makes it be this way way? Is it the ferromagnetic material? If so, why? If the core was made of completely vacuum would the leakage be 100%?

Guys,I need to calculate the flux and current of neutron by MCNP.So what's the difference between them ,and How to calculate them? Any ideas?

Suppose we have placed a cube in field which varies linearly with z axis so electric field magnitude on coordinates of face ABCD is clearly more than face EFGH and we know area of both faces are equal, So if we calculate flux then it would be non zero but it contradicts with the fact that...

Forgive me if a similar thread has been posted before... I was doing some questions and I just noticed an apparent discrepancy in how the term "flux" is thrown around. In the context of surface integrals, the scalar result is usually termed the flux whilst the vector field is termed the flux...

From the density and the mass we can find the volume using d=m/v <=> v=0.06 m^3. Since we consider the astronaut a sphere we find his radius using V(sphere)=4/3*π*R^3 =>R=0.242m. Now we can calculate the surface area with the formula A=4πR^2=0.735m^2. The energy absorbed will be i suppose equal...

a) \vec{F}=\vec{E}\cdot q \phi =\oint \vec{E}d\vec{S}=\oint \vec{E}d\vec{S}=\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \perp}+\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \parallel}=0+\oint EdS\cdot \underbrace{\cos 0}_1= E2S \dfrac{Q_{enc}}{\varepsilon_0}=\phi \left...

I am having trouble figuring out if the circular loop has an induced current. One explanation is ∫ E ds = -d Φ / dt. Since flux = B ⋅ A, a change in the magnetic field would require a change in the magnetic field, a change in the area, or change in direction of either vector. Since none of...

My attempt is for part a a. The electric field is into the base of the hemisphere and the area vector is coming out of the base Θ=180 Area of base of the hemisphere is = π * r^2; Hence the electric flux ∅ = ∫ E.dA; ∅ = E*π*(0.0568^2)*cos(180) = -2.5*π*0.00322= - 0.0253N.m2/C; b. For the part...

Hi, I just have a quick question about a problem involving Gauss' Theorem. Question: Vector field F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} has net out flux of 4 \pi for a unit sphere centred at the origin (calculated in earlier part of question). If we are now given a vector...

Let ##S_t## be a uniformly expanding hemisphere described by ##x^2+y^2+z^2=(vt)^2, (z\ge0)## I assume by verify they just want me to calculate this for the surface. I guess that ##\textbf{v}=(x/t,y/t,z/t)## because ##v=\frac{\sqrt{x^2+y^2+z^2}}{t}##. The three terms in the parentheses evaluate...

In order to flux-pin a piece of type-II superconductor in a magnetic field, the piece of superconductor is held in place within a magnetic field and supercooled. Let's say that Bp is the B-field within the superconductor as it is being pinned. After pinning has been carried out, is it correct...