Flux Definition and 1000 Threads

I am currently studying a section from \textit{Electricity and Magnetism} by Purcell, pages 81 and 82, and need some clarification on the following concept. Here’s what I understand so far: 1. The integral of a function $ \mathbf{F} $ over a surface \( S \) is equal to the sum of the integrals...

Flux equals dot product of Area Vector and the Field vector. So the areas are 3. The projection of cylinder (shadow of cylinder). It's flux is E2HRcostheta. Then remaining two circles have flux Eπr²sintheta each. But I checked my solution book and they have considered only half areas of the top...

TL;DR Summary: Confusion in φ cap direction for Left & Back face The image of the question is shared at this Imgur link - The only issue I'm facing in this particular problem is in calculating the flux through the "Left" & "Back" faces of this quarter cylinder. More specifically the issue is...

Hello! I have a question regarding the mutual inductance of two coils in a transformer. In the formulas for linked coils ##M=k*\sqrt{(L_1*L_2)}## where ##k=1## for a perfect coupling. I wanted to check my understanding about mutual inductance and see how it can be determined. When I vary the...

I am not sure why latex is not rendering, but here is the question. The answer is ##\frac{a^2}{8}## and for the love of my life, I don't know how. Can you please help me with this?

If Shielding is required for gamma ray flux of 1e23 (let say E=1 Mev). As Shielding cannot fully attenuate flux to zero, how much percentage is technically recommended for shielding of above flux?. So far as I know shield thickness is considered to minimise dose/flux Upto 1/10 of its...

Magnetic flux density(B) is defined as, magnetic force per unit pole strength and flux is defined as magnetic field passing normally through given surface. I think, I am clear about these definitions, and quantitative meaning they carry. I usually find, in some texts, the definitions as in image...

Can any one please explain if I want to run mcnp 5 input file of certain geometry for flux calculation on different surfaces. So far as I know If I increase the NPS (number of particles) it wll give more accurate result but when I increase NPS from 10e9, input file do not run and close within a...

I could not find any derivations in the litterature, except for the expected value of the energy flux expression itself: $$\overline{\Phi_{effusion,\epsilon}} = \overline{\dot{N_{ef}}}\overline{\epsilon_{ef}}=\frac{3Nl}{2A}\sqrt{\frac{(k_BT)^3}{2\pi m}}$$ I've started off by calculating the...

Hi I am designing a flyback converter. The calculation (.jpg file) is based on Daniel W. Hart Power Electronics book. The transformer model consists only of an ideal transformer and its magnetizing inductance (or "primary inductance" in some textbooks). The datasheet of the transformer's core...

I believe this does has a couple of Calculus aspects to it but I don't really know how I'd find the surface area of inside the bowl. The answer sheet says the answer is 252 with a margin of error of +/- 1

Alfvén’s theorem is very famous in plasma physics. It is also often used in astrophysics. The link in Wiki: https://en.wikipedia.org/wiki/Alfv%C3%A9n%27s_theorem However, after a series of continuous reasoning, it seems that this theorem has problem. What errors can be hidden in the reasoning...

As stated in the problem, I want to demonstrate mathematically that field line density is directly related to the magnitude of B. How would I be able to do this, other than simply using the flux equation and showing that for a higher flux in the same area, the magnetic field must be rise...

For the problem attached, Why is the magnetic Flux not zero through the loop? Many thanks!

In the derivation of the conservation law of the conservation of mass, the flux on one side enters and the flux on the other side leaves the control volume. I presume this is due to the assumption that the volume is infinitesimally small and hence v(x,y,z,t) will not change directions...

For this problem, The solution is, However, why can the differential area not be: I tried integrating and got, Can someone please tell me what I have done wrong? Thank you!

Flux=$$\iint(xz, -yz, y^2)\cdot(x,y,z)/\sqrt{2} dA=\int_0^{2\pi}\int_0^1 r^2\cos^2\theta \sqrt{1-r^2/2} rdrd\theta$$. Integrating this doesn't give the correct answer of ##\pi/4##.

What is the flux density of salt in a horizontal tube 10 cm in length connecting seawater (salinity = 30 g/l) to a tank of freshwater (salinity ~ 0) assuming no advection occurs?

I recently performed an experiment that involved using a cylindrical scintillator to detect cosmic ray muons by observing the amount of particles that decayed within 20 microseconds over a long period of time. I'd like to use this to find the flux of muons at my scintillator so that I can...

Sorry if I post again about this topic (last time I promise!) but I still have some doubts regarding the concept of flux. This collection of problems I have quite standard but there are so many variations. Here is the circuit in question: Something tells me that I could write a function that...

$$B(t) = B_{0} \frac{t^2}{T^2}$$ for ##0 \leq t \leq T## The issue here is more conceptual, because once I find the flux of B I know how to proceed to find the current. I got velocity (but it seems to me that it is the initial velocity), I could use it to find the time in function of space...

Hi, I wanted to find the number of protons striking a surface area during a solar event and the units provided are: #/(cm^2 s sr). Say I have a 1 m^2 surface area directly facing the sun, how do I use those units to discover the number of protons/s. What is the value of the solid angle to...

Hi everyone, I have a EE problem that I need to sort out for alternating voltage. I have to find out the maximum flux density. B_max= integral from 150 degrees to 30 degrees (u/(2NA) dt is my problem. I have a hard time to integrate this since I am to integrate with time and not degrees or...

The vectorfield is $$A = grad \Phi$$ $$A = x^2 + y^2 + z^2 - (x^4 + y^4 + z^4 + 2x^2y^2 + 2x^2z^2 + 2y^2z^2)$$ The surface with maximum flux is the same as the volume of maximum divergence, thus: $$div A = 6 - 20(x^2 + y^2 + z^2)$$ This would suggest at the point 0,0,0 the flux is at maximum...

In Sakurai Modern Quantum Mechanics, I came across a statement which says probabiliy flux integrated over all space is just the mean momentum (eq 2.192 below). I was wondering if anybody can help me explain how this is obtained. I can see that ##i\hbar\nabla## is taken as the ##\mathbf{p}##...

Hello All, Please see the attachments. The pdf file is the IEEE paper I'm reading. Figure 1 show a slot of the AC machine similar to the front view of the picture below: But in one slot, they fit two sets of conductors. The first set carries current i1 in total. The second set carries...

During a reactor assembly calculation, I need to determine axial and radial flux distribution over the surface. When I use F2 and F4 tally I get some value with unit 1/cm**2 What does the value means, neutron flux is supposed to be in the 10^14 range but output values are 10^2 range. Can anyone...

My attempt: We have 3 charges inside 2 +ve and 1 -ve so i just added them up. 4 + 5 +(-7) = 2q Then there is a -5q charge outside the sphere. I did 2q + (-5q)= -3q . The electric field flux formula is Flux= q/ E0 . So i got -3q/E0 which is obviously wrong : ) . After quick googling , I...

Short version: problems fixing 25-year old world-building; due to canonised data points, I have a planet that is way too hot to work, compounded by interpretation problems by teenage-me on stellar data - help would be appreciated! Sometime in around the mid 1990s, I got SpaceMaster the RPG (and...

The magnetic flux ##\phi_m = \int{BdA}## The magnetic field of the coaxial cable B = ##\frac{I_{enc} \mu_0}{2\pi r}## since surface area of a cylinder = ##2\pi rdr L, dA = 2\pi L dr## where L is the length of the coaxial cable so ##\phi_m = \int{\frac{I_{enc} \mu_0}{2\pi r}2\pi L dr}##?

Hi, I am willing to simulate a 3D ferrite bar transmitter and reciever where coupling coefficient k and Bt magnetic flux density on the each side uses the finite element method for solving partial differential equations. The Magnetic Fields module has equation (jωσ − ω2ε0εr)A + ∇ × H = Je...

If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could...

I think the issue is how I parameterize my vector field, but not quite sure. In case you were wondering, this is problem # 27, chapter 16.7 of the 8th edition of Stewart. Thanks for any help.

1) Why is the electric field 0 at the bottom of Gaussian surface? Isn't the electric field on both sides of the surface, pointing down and outwards like a plane of charge? see image. 2) Why does a charge distribution with cylindrical symmetry have to be infinitely long? 3) My book says a...

I am confused at this calculation of the electric flux through a trapezoidal surface. The flux in should equal the flux out. The flux in equals -E*A1 where A1 is the area of the bottom of the trapezoid. The flux out equals E*A2 where A2 is the area of the top of the trapezoid. But the two fluxes...

1)Field Lines is supposed to represent the electric field around a charge ,now we can draw infinite field lines around a charge and sinc Electric flux is No of Field Lines /area ,does it become infinite ,the whole concept of field lines is quite in the Gray Area for me ,I can in theory mark...

I am doing a project, actually it is a simulation. And we aim to determine the spatial and heat flux evolution of the system. The system consists of two concentric cylinders separated by an insulating material. I change the value of kappa of the insulator but the heat flux remains always the...

On the Internet, I have read that the energy doesn't flow in the wire, for example in a very simple electric circuit made of a battery and a closed loop. When one computes the Poynting vector ##\vec S \propto \vec E \times \vec B##, one gets that its direction is towards the center of the wire...

a) $$\phi_T=\phi_F-\phi_I=10^4\cdot 4\cdot 4-10^4\cdot 4\cdot 4=0\, \textrm{Nm}^2/\textrm{C}$$ b) $$\phi_F=\underbrace{300\cdot 4}_{\vec{E}}\cdot \underbrace{4\cdot 4}_{\textrm{area}}=19200\, \textrm{Nm}^2/\textrm{C}$$ $$\phi_0 = 300\cdot 0\cdot 4\cdot 4=0\, \textrm{Nm}^2/\textrm{C}$$ Then...

Summary:: A 4.3 mH toroidal inductor has 100 identical equally spaced coils. If it carries an 11.6 A current, how much magnetic flux passes through each of its coils? Express your answers in milliwebers. 4.3 mH= (Wb/A) 100= N 11.6= I Φcoil= ? So from my observation of another question...

Picture for better understanding. My answer : I want to know how to solve this problem without using cylindrical. I mean how can we solve this using cube and its sides. Thanks.

Question: Equation: Attempt: Can someone verify my answer?

Question: Equations: My attempt: Could someone confirm my answer please?

Assuming that the observer moves along the direction of the light, does the speed of the observer's measuring instrument relative to the light source (which may be close to the speed of light) affect the brightness and/or power flux density measured by the observer? I'm not sure about this...

My general understanding of electric flux density is 'electric flux per unit area'. This gives the SI unit N/C. But According the formula of electric flux density, D=eplison*E, the SI unit is C/m^2. How come the dimension in both cases not matching if both are true?

I have read three definitions of electric flux in textbook which is confusing me.. 1. Electric flux is the number of electric lines passing through any area of a surface. 2. Electric flux is the number of electric lines passing through unit area per second held perpendicularly. 3. Electric flux...

Question My attempt for the 1st part, when r = 1.5 m Could someone confirm my answer?

Relevant Equation: My attempt: Could someone please confirm my answer?

Hi guys i have some concept issues about flux. My book says flux is proportional to the number of lines passing through that area. so my question is: first i am thinking that a 2D circle which has a 2r diameter and it is enclosing a 2q charge so its flux should be 2q/Epsilon.then i am thinking a...

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