Density Definition and 1000 Threads

Is it possible to calculate the average number of Cooper-pairs, existing at any given moment, per cubic centimeter of niobium (or YBCO), at their critical temperatures? I realize that Cooper pairs form and dissolve continuously, and constantly change partners, so perhaps its not easy to...

In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over...

From the view point of quantum field theory how does one describe the electromagnetic energy density between the plates of a charged capacitor? Thanks!

Hello, I am an electrical engineer rather than a physicist, however, I am trying to understand the physics of a twin wire transmission line in terms of the charge and current density. Let's say we have a lossless, infinite length, twin wire transmission line, a step current is induced into the...

In Newtonian physics, is the current density, usually called j, a vector? Namely, is it a polar vector in the sense of a tensor of rank 1?

Homework Statement I'm confused about the following kind of situation. Consider a block of density ##\rho_b##, mass ##M_b## and section ##S_b## that floats on a liquid of density ##\rho_l##, in a tank of section ##\mathcal{S}##. On the block there are some objects (all equal), of density...

Hello, I'm stuck with this exercise, so I hope anyone can help me. It is to prove, that the density of states of an unknown, quantum mechanical Hamiltonian ##\mathcal{H}##, which is defined by $$\Omega(E)=\mathrm{Tr}\left[\delta(E1\!\!1-\boldsymbol{H})\right]$$ is also representable as...

When I read that conditions were such and such 1 to .05 seconds after the big bang, is that duration somehow longer than 1/2 second is now (maybe because of the difference in density or like the twin paradox?)?

Can any expert help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system. $$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2}) & cos(\frac{\alpha}{2})+sin(\frac{\alpha}{2}) \\ 1 & 1 &...

It seems by this paper that there are more black holes than expected, so what is the expected density of black holes in the nearby universe? arXiv:1606.04996 (cross-list from gr-qc) [pdf, other] Constraining modified theories of gravity with gravitational wave stochastic background Andrea...

Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...

Homework Statement A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring. https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif Its circular surfaces are horizontal. What effect will the...

Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...

Hi, in gravitational theory the action integral is: I = ∫( − g ( x))^1/2 L ( x) d 4 x, but I do not know why there is a square root -g . Could you give me the proof of this integral? I mean How is this integral constructed? What is the logic of this? Thanks in advance...

Homework Statement A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 2.53 hours. What is the density of the planet? Assume that the planet has a uniform density. Homework Equations T^2=(4pi^2r^3)/GM V=4/3piR^3 Density= Mass/...

Hi, I know how to calculate density of states for both cases, but it is not clearly to me how I can go from 3D case to 2D. I have energy from infinite potential well for 3D $$E=\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{l_x}+\frac{n_y^2}{l_y}+\frac{n_z^2}{l_z})$$ let make one dimension very small...

Hey guys, I just wanted to check if my method for solving this problem is correct. 1. Homework Statement Consider an annulus with inner radius R1 and outer radius R2. The mass density of the annulus is given by σ(r)=C/r, where C is a constant. Calculate the total mass of the annulus. Homework...

I am trying to calculate the flux density of an air gap in an electromagnet. I am following this page that calculates the flux density in a C core with an air gap. My confusion is that I am using 50Hz AC instead of DC I have control over the voltage amplitude since I would be using a variac to...

Hello! When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components k_x = \displaystyle \frac{\pi}{L_x}p k_y = \displaystyle \frac{\pi}{L_y}q k_z = \displaystyle \frac{\pi}{L_z}r...

What has a higher density? Black Holes or Singularities? I looked online and all I saw was that they both have infinite densities.

Had an argument with a few guys at the gym today. I told them that loading a barbell with 100 on each side instead of 2 45s and a 10 causes more pressure on your spine. This example is in reference to someone performing a low bar squat in which the bar has contact points across the entire back...

Its said that if there are different pocket universes made by inflation then this solves the alleged fine tuning of dark energy. My question is this: can the idea of different values for the vacuum energy density in these different pockets be derived from quantum field theory or does it need...

It says in Susskind's TM: ##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}## with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?

So if a car were to somehow have its density lowered by lowering the mass, but keeping the volume the same, would the car be more damageable and breakable than it was before, or would that depend on something else other than density?

How is a top gate used to change electron density in 2D semi conductors? I get the principle, you are just shifting the chemical potential by some voltage so that there are more or less electrons in the specific bands. But how is it physically done? Thanks.

Hello everybody, Is there a way to calculate/predict the electron number density of a plasma? Thanks in advance

Homework Statement Given a sphere with radius R, centered at (0,0,0), it's dipole density given as ##P\left(\vec{r}\right)=\alpha\left(R-r\right)\hat{z}## where r is the distance from the center of the ball. I'm required to find: Bound charge density inside the sphere, bound charge density on...

I want to use the equation: Fr='gamma'*distance from centroid*Area but the example is showing density in N/m^3 while I only have the density in kg/m^3 Does this mean I have to multiply it by 9.81 to get the right answer? Thanks.

Hello, let be ##x \in \mathbb{R} - \mathbb{Q}##, do we have de density of ##\{nx - \lfloor{nx} / n \in \mathbb{N}\}## in ##[0; 1]## please? I think yes but it's just an intuition : if I take a and b in ##[0; 1]## with a < b, I have an irrationnal between them let call it c but I don't know...

I have a Stats exam on Wednesday and while I thought I was quite well-versed, I've gone back over to the very basics only to find myself confused at what should be introductory. Suppose I have a continuous random variable modeled by a probability density function: $$f(x)=2x$$ Obviously the...

The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law essentially uses the fact that, if ##\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3##, ##\boldsymbol{J}\in C_c^2(\mathbb{R}^3)##, is a compactly supported twice continuously differentiable field...

Homework Statement A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.[/B]Homework Equations For canonical ensemble ##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}## In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|## The...

I'm doing a question relating to the pressure inside on object submerged in water. Here is the question: A tube, height 1.2m, is submerged vertically in the ocean where the waters density is 10^3 kg/m^3. A diver initially holds the tube vertically directly on top of the water. He then dives to...

[Mentors' note: split off from this thread] Do all black holes have the same density?

Hello all, I am currently trying to convert brine salinity values in ppm to the corresponding brine density. My understanding is that I can do that using ppm * SG = mg/L . However I do not know how to get the Specific Gravity (SG) of my brine. The data I try to convert has a minimum value of...

Magnetic flux density B is a vector quantity and thus represents a force. However most texts state that the magnetic force is perpendicular to the direction of B, which is tangential to the magnetic field line at any give point. I assume that this magnetic force refers to the Lorentz force. So...

Homework Statement The Lagrangian density for a massive vector field ##C_{\mu}## is given by ##\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\frac{1}{2}m^{2}C_{\mu}C^{\mu}## where ##F_{\mu\nu}=\partial_{\mu}C_{\nu}-\partial_{\nu}C_{\mu}##. Derive the equations of motion and show that when ##m...

Homework Statement Homework Equations m = ∫∫sρ(x,y,z)dS The Attempt at a Solution I used polar coordinates for this (is that necessary here)? I found zx and zy, took the cross product of those, and found it to be √(2). So dS = √2 dA. √2 ∫02pi∫25r2drdθ = 78pi√2

1. Homework Statement A block of wood has a mass of 3.47 kg and a density of 628 kg/m3. It is to be loaded with lead (1.13 × 104 kg/m3) so that it will float in water with 0.848 of its volume submerged. What mass of lead is needed if the lead is attached to (a) the top of the wood and (b) the...

Q: What was the average density of the universe at the time the light was emitted by the z = 6.56 galaxy? For the question we know the current average density of the universe and red-shift wavelength z = 6.56. It says to calculate the average density of the universe at the moment when light was...

Homework Statement A thin rod of length 2L has a linear charge density that isλ0 at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero. Given E = −kλ0/L(d/(L−d)−ln(d−L)+d/(L+d)+ln(L+d)) for a point P that is...

If dark energy density were to be very slowly decreasing, how will the fate of the universe be any different from the energy density being constant? Would not the energy density be completely dominant in the future even if it were to be very slowly decreasing?

Homework Statement Current density is the amount of current per cross sectional of flow. I'm having trouble wrapping my head around this definition. Surface charge or volume charge I understand better since they are almost analogous to the density we all understand (amount of matter/charge...

I am conducting an experiment that rotates a sealed donut cylinder to investigate amongst other things the inertia of the contained fluid. Process I rotate the cylinder to a set speed (assuming that the viscosity of the internal fluid will end up rotating the fluid to solid body rotation) then...

We have ## \rho ## and a hamiltonian K on ## H_s \otimes H_E##. have we (K \rho)_S \otimes Id_E = K (\rho _S \otimes Id_E) ? here ## \rho _ s ## and ## (K \rho) _ s ## are the reduced density matrices. If P maps an operator O to ##O_S \otimes Id_E##, I have to prove that ## PK \rho = KP...

Homework Statement Copper and aluminum are being considered for a high‐voltage transmission line that must carry a current of 51.4 A. The resistance per unit length is to be 0.176 Ω/km. Compute the magnitude of the current density for an aluminum cable. Homework Equations R\quad =\quad \frac {...

Homework Statement A beam contains 3.95×108 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.64×105 m/s. What is the magnitude of the current density? Homework Equations J = nev n = electron density e = electron charge v = drift velocity The...

Homework Statement Problem from the book "Engines, Energy and Entropy", Page 55, question 7 has me stumped. It doesn't feel like their is sufficient information to work out the mass of the air. They've given us density (as seen in the picture, if the upload works) , which is mass over volume...

Hi, If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy between $E_0$ and $E_0 + \delta E$. In the limit of large quantum numbers, the result is well...

I got (very) confused about the concept of states, pure states and mixed states. Is it correct that a linear combination of pure states is another pure state? Can pure (and mixed) states only be expressed in density matrices? Is a pure state expressed in a single density matrix, whereas mixed...