Relationship Definition and 999 Threads

Well, I didn't know where to post this rather philosophical stuff, so decided to put it here. But I promise it is related to all sciences mentioned above. Here is the setting. Whenever we prove something mathematically, we always think that the proof is "eternal", often contrasted with the...

So I've been simulating a really simple geometry using ANSYS Maxwell. It is a cylinder only and I am looking at the \overrightarrow{B} and \overrightarrow{H} fields in order to see their relationship between them when the material is magnetized in the circumferential direction. I used a...

From the Greiner (Thermodynamics and statistical mechanics) on the relationship between the number of microstates of two systems and the total entropy: ...for two statistically independent systems the total number of compatible microstates \Omega_{tot} is obviously the product of the...

Is there a proof or obvious reason why the vertex function is related to the current via: S(p')\Gamma^\mu(p',p)S(p)=-\int \int dxdy e^{ipx}e^{-ipy} \langle T \psi(x) j^\mu(0) \bar{\psi}(y)\rangle In the free-field case one can see it's true. But the interacting case?

Why is V=fl a "dispersion relationship"? I've heard of V=fλ being referred to as "the simplest dispersion relationship", however it seems to be used to describe non dispersive traveling and standing waves, where the wave velocity is determined by the medium (fixed) and either f is a dependent...

Hi everyone, I am curious as to whether it is possible to calculate the difference in density due to applied (mechanical) stress on an object. E.g.: apply a controlled force of, say, 50 N on a structure, calculate the mechanical stress in the object with sigma = M/I * z and then go on from...

So I noticed we can define entropy in two very different ways: 1) quantum mechanically S = -k Tr(\hat{\rho}\ln{(\hat{\rho})}) 2) classically S = -k \int \rho \ln{(\rho)} d\Gamma where Tr is the trace and d\Gamma = \frac{1}{h^{3N}N!}\prod_{i}^{N} d^{3N}q_{i}d^{3N}p_{i} is the phase...

Q1. A spectrometer measures the optical power spectral density as a function of the wavelength or optical frequency (say F(v) v.s. v, where "v" is frequency), is this right? Q2. An interferometer can be used to detect the amplitude of a light source v.s. the path difference (x), i.e. if the...

Hello all, I'm new to the forum so I hope I'm posting this in the correct section. I'm currently conducting an experiment in which I'm examining how the dielectric constant of a binary mixture changes with concentration and temperature using a parallel plate capacitor for measurements. The...

I have been with my girlfriend for about a year and 7 months. I love her and feel very emotionally attached to her and her to me. But recently I have been attracted to this other girl. I don't really talk to the other girl because I fear that if I do I'll become more attracted to her. She's...

I usually do not ask for this kind of stuff, but this time I really have no way to verify if this is correct(and it has to be). So here it goes: On a subcritical nuclear reactor with 100 fuel elements we read the signal of 10e-9 A. When we add 10 more fuel elements, signal jumps to 10e-8 A. How...

$$ \int_0^{\nu}\frac{d\nu'}{(1 + e\cos(\nu'))^2} $$ Consider \begin{align} \frac{d}{d\nu'}\frac{\sin(\nu')}{1 + e\cos(\nu')} = \frac{\cos(\nu') + e}{(1 + e\cos(\nu'))^2}\\...

The resistance of wire A is four times the resistance of wire B. Calculate the ratio of the radii of the wires

This is from Hogdson's book the Mind Matters Does anyone know what the actual equation he is talking about and I was wondering if anyone could give me a few more details regarding the energy-time uncertainly relationship.

Homework Statement Use the Stokes' Theorem to show that \intf(∇ X A) dS = \int(A X ∇f) dS + \ointf A dl Homework Equations Use vector calculus identities. Hint given : Start with the last integral in the above relation. The Attempt at a Solution To be honest, I really don't know...

First of all, if you have a generator with an open circuit, and you are pedal powering it, where does the energy go? I would say it is lost as heat, but not sure what could heat up. The coils in the generator itself? Next, what happens if you short the output of a generator? Does it make it...

Homework Statement If we define \xi=\mu+\sqrt{\mu^2-1}, show that P_{n}(\mu)=\frac{\Gamma(n+\frac{1}{2})}{n!\Gamma(\frac{1}{2})}\xi^{n}\: _2F_1(\frac{1}{2},-n;\frac{1}{2}-n;\xi^{-2}) where P_n is the n-th Legendre polynomial, and _2F_1(a,b;c;x) is the ordinary hypergeometric function...

hi guys, I'm currently working on a physics report about a simple pendulum and can't figure out how to answer one of the questions: 3. "define all terms in the solution(x(t)=Acos(ωt)) and especially the relationship between angular frequency, and periodic time, T." ive defined all the...

Hi, I was wondering how to derive relationship between radiocative constant and half life, which is t1/2=ln2/b, where b=decay constant. It seemed like the it was just replaced into the equation A=A0(1/2)t/t1/2. Thanks in advance

Hello Everyone, I am having a very difficult time intuitively understanding the formula -dU/dx = Force(x). I don't want help deriving it, I'm simply looking for an intuitive understanding about why this might be true. An example with gravity would really help. My thoughts so far: I find...

Is the relationship between the length of a guitar string and the frequency of the pitch it produces a linear relationship? e.g. If the frequency of the pitch of a string is 60 Hz and I halve the length, should it produce a pitch with a frequency of 120 Hz? This is assuming all other...

Sorry if this is in the wrong place. Was not sure what it is categorised as. I have come across the following:e^{-\frac{\omega}{c} nkz}, referring to attenuation of a wave. It was found here...

If you think about a double-napped cone, and the various non-degenerate sections you can get with it: 1. Circle 2. Ellipse 3. Parabola 4. Hyperbola, you can see that there is a progression here: increasing angle $\alpha$ that the intersecting plane makes with the horizontal. To be clear about...

A negative particle is moving in a uniform magnetic field pointing in the negative k direction. The force on the particle is -i and j. Find the x and y components of velocity. (I left out the numerical data in the question). I used F=q*v*B and in order to find the x component I used the F in the...

E(lux), I (candelas) , r(meters) E=I/r^2. What is this formula ? I got it from a photovoltaic cell experiment. Use solar cell connect to a micro ammeter to detect the current produced due to the intensity of the light source. The bigger the r , the lower the current. how does the formula...

If a,b are positive integers and (a1/2b1/3)6 = 432, then what is the value of ab?

Below is a attempt at a proof of a distributive property of union/intersections of sets. A critique would be very much appreciated. Thanks in advance! ----------------- For sets A, B, and C, the formula, ##A \cup (B \cap C) = (A \cup B) \cap (A \cup C)## is true Two sets are equal if they...

I'm not sure I get how:\frac{\mu_{0}}{4\pi}\int_{C}\frac{I(d\vec{l}\times\vec{r})}{r^{3}} = \frac{\mu_{0}}{4\pi}\int_{C}\frac{I(d\vec{l}\times\hat{r})}{r^{2}} the r is a displacement vector in the first, and in the second it's a unit vector, but why is this so?

Hi, I've recently taken a Calculus 1 (Differential Calculus) course and I've been looking ahead to see what sort of material is covered in the Calculus 2 (Integral Calculus) course. I am wondering about the relationship between derivatives and integrals. From what I understand, an integral...

What is light doing to make us believe that space is boundless but also finite (if I have Einstein's thinking right)? There's something tricky going on here. Are there points (coordinates) in space that are not reached by light?

Star Mass how can affect of event horizon. Because I think singularity affects event horizon not mass.

Wondering if anyone has developed a scaling heuristic for the relationship between size of accelerator and smallest size that can be probed with it. With so many data points, something ought to emerge, perhaps a modified power law. Adding a time axis could make a Moore's "law" projection for...

If a shear force is acting on a rectangular beam, how do I use the value of the shear modulus to calculate if the force applied will fracture the beam? Below I've submitted the data involved. The shear force applied is 1000 N and the cross section area is 28 mm. So the shear force applied is...

Homework Statement Without a graph, test the suggestion that the speed, c, of the water wave is related to water depth, d, by: c ∝ d^1/2 No other data is given, this is suppose to be collected by myself but I am revising for a practical exam paper without having the data given. Markscheme...

1. Homework Statement If \phi is a usual field is it possible that H\dot{\phi}=-\partial^2\phi/{\partial x^2} Where H is the Hubble constant and the dot denotes time derivative 2. Homework Equations H\dot{\phi}=-\partial^2\phi/{\partial x^2} 3. The Attempt at a Solution I tried different...

Currently in 2nd semester electronics engineering, last semester I ended a 6 year relationship (I'm 25) I was thinking of trying not to get on a new relationship while I studied my career to focus just on school for now, what are your thoughts on this? I was studying graphic design/working and...

Homework Statement There's no specific problem here so I'd say this template doesn't specifically apply. I'm doing a piece of coursework investigating F=BIL and electromagnets and I'm having some trouble. I think the issue here is the data that I've collected so bear with me. I've been making...

Can someone please explain WHY the statement below is valid: s = σ + jω ; left hand side σ < 0 So it basically says if all the poles have negative real parts then we can directly substitute s = jω to get the Fourier transform. This doesn't make sense to me, does it make sense to you...

I'm way outside my realm of knowledge here so perhaps I need some help polishing my question or the concepts behind it. Thank you for your patience. Does the orientation of circularly polarized light (CPL) as a reaction mechanism influence the chirality of the molecule in a general manner...

instead of typing it out, here is the problem I know what to do, my math just isn't good enough to combine the equations properly. Been at it a few hours, brain hurts, please help!

Homework Statement The critical angle for total internal reflection for a substance is 58.0°. What is the polarizing angle for this substance? Homework Equations Index of refraction: n = 1 / sin(θ_{c}) and n = tan (θ_{p}) The Attempt at a Solution So I plugged in the numbers for...

Homework Statement "Sketch the V_o vs V_i relationship for a voltage controlled voltage source amplifier" Homework Equations none really The Attempt at a Solution Ok, so I understand and know by heart the ideal and the practical relationships for a (respectively) ideal and...

I'm currently reading through a textbook by David Miller and attempting to teach myself quantum mechanics to assist with my electrical engineering. I have run into a little trouble trying to understand how the probability current satisfies the continuity equation with a probability distribution...

Homework Statement Two capacitor plates (infinite plane) with uniform charge distribution but different charges (one positive, one negative) are distance "d" apart. A charge is place at d/2 and feels force |F1|. A charge is placed at d/4 and feels force |F2|. How does |F1| compare to |F2|...

Homework Statement 1. fh stands for energy of a particle. But what is included in the energy ? K.E. of the particle only ? 1.1. If fh is the K.E only, then I have a question. λ=h/p --> fλ=fh/mv --> mv^2 = fh. It is strange that fh = mv^2 but not 1/2 mv^2. 2. Is broglie wavelength equivalent to...

Hi, This might be a silly question but I've been struggling to find this out. What is the relationship between dose rate and the amount of Cs-137 in an area? if I know the exposure dose of the area is 5mSv, how can I work out how much Cs-137 is in this area? Thanks

Homework Statement The quantity p varies directly with the cube of q and inversely with the square of r. If p = 3/2, q = 1/2, and r = 1/3, which of the following equations represents the relationship between p, q, and r? Homework Equations Here's what I did... (3/2)p = (1/2)q^3...

what is the relationship between these 3 Charge Capacitance voltage?

(I'd like to preface this with the warning that the following question may be a very dumb one.) My understanding is that current density (or flux) \vec{J} = \vec{J}(x, y, z) is the rate of flow of charge (or the current) per unit area. (Units of \frac{\text{C/s}}{\text{cm}^2} .) Say...

We know that the Young's modulus of an object is defined as the ratio between its stress and strain: Y = σ/ε , or: Y = F*L/A*ΔL We also know that Hooke's law, which can be applied to any linear elastic object, can find spring constant: F = k*x , rearranged: k = F/x But is...