Density Definition and 1000 Threads

Homework Statement Given the electric potential ##V(r)=A\frac{e^{-\lambda r}}{r}## calculate the charge density ##\rho(r)## and the electric field ##E(r)##. They specify the answer for charge density should be: ##\rho = \epsilon_0 A(4\pi \delta^3(r)-\lambda^2e^{-\lambda r}/r)## Homework...

Hello! I am a bit confused about calculating the induced surface charge density on an infinite conducting plane, with 0 potential, in the presence of a charge, q, a distance d above it. Assuming that the plane is in xy plane and the charge in positive z region, in the book they use the method of...

Homework Statement The potential difference between the surface of a 2.2 cm -diameter power line and a point 1.9 m distant is 3.8 kV. What is the magnitude of the line charge density on the power line? Express your answer using two significant figures. Homework Equations V =...

Homework Statement Hi, So I'm doing a electromagnetics course and we've been given equations for electric flux and electric flux density but I can't seem to find any sort of intuitive explanation for these. In my lecture notes, the electric flux density is introduced first as vector D and...

Homework Statement The electric field strength just above one face of a copper penny is 2230 N/C. What is the surface charge density on this face of the penny? Homework Equations Electric field of an infinite plane of charge = η/(2*ε0) The Attempt at a Solution I used the above equation, and...

Homework Statement We're given pressure (Which is mass/volume) and G constant Looking for minimum r, given pressure, that would produce a certain F value in Newtons... 2. Homework Equations F=ma Blanking here* Honestly everyone this is my first physics intense college course and i have no...

Homework Statement A metallic film has length L=10mm, width W=1mm and thickness t=1##\mu m##. The current is parallel to the long edge and has magnitude ##I=0.7A##. Longitudinal voltage is ##V=1V## and it doesn't change with magnetic field. The Hall (transverse) voltage ##V_H## increases at...

Homework Statement Two 10-cm-diameter metal disks separated by a 0.64-mm-thick piece of Pyrex glass are charged to a potential difference of 1100 V . What is the surface charge density on the disks? What is the surface charge density on the glass? Homework Equations C=(e_0A)/d C=Q/V charge...

Homework Statement ##e_{r1}=2## ##e_{r2}=10## ##α_1=\pi /4## ##D_1=100 nC/m^2## ##ρ_s=0## On the borderline of two dielectrics there is no free charge. Calculate the surface bond charge density of both dielectrics. ##ρ_{bs1}=?## ##ρ_{bd2}=?## Homework Equations 3. The Attempt at a Solution...

Dear Forum, The title "Speed of time" is the best I can come up with. We know that time isn't constant, rather it depends on the speed at which we move as well as the gravity we are subjected to (see https://en.wikipedia.org/wiki/Gravitational_time_dilation for a reference to the latter). As a...

Homework Statement Homework Equations E=σ/(2Eo) σ=2Eoma/e a=Δv/Δt The Attempt at a Solution So doing my best to read the velocity over time graph I came up with Δv/Δt=(-2E5m/s)/(10E-12s)=-2E17 m/s/s σ=2Eoma/e =2(8.99E-9C)(9.109E-31kg)(-2E17m/s/s)/(1.6022E-19) =-0.020444 C/m^2 but by the...

Hello, I would like to know how to calculate the negative energy density in the region between two Casimir plates, given a distance between two parallel plates. Thanks, much appreciated!

Homework Statement Q6. A function, ##f\left(x\right)=\frac{ax+1}{\left(ax-1\right)^3-\frac{a}{\left(x-1\right)^2-1}}##, can be defined as a PDf over the domain ##(0, 2)##. Express answers to 4 decimal places unless specified otherwise; (a) Find the value of ##a## given that ##f(x)## is a PDf...

The continuity equation in fluid mechanics is: Do the condition of "constant-density fluid' and 'imcompressible flow' have the same effect on the continuity equation, in that the first two terms disappear? Or is there a difference between these assumptions?

Homework Statement Two hollow metal spheres (left one has radius of 0.7 meters and right one has radius of 0.4 meters) are half-submerged in the sea water with specific conductance of γ = 4 S/m. Distance between their centers is much greater than their radii dimensions and equals 60 meters...

Special relativity states that according to an observer at rest, a measuring stick on a moving platform will appear shorter. Would this observer still see the measuring stick as comprising of the same amount of atoms as the observer who is at rest with respect to the measuring stick? If this is...

Homework Statement Hello- I'm having trouble understanding a problem: Consider a sealed 1D pipe of length L. At t=0, v=0 everywhere and the pressure is given by: P=P_0 +δP and δP = (p-bar)x/L P_0 and (p-bar) are both constants. and I'm supposed to find density (ϱ) as a function of x and t...

I am busy with an effort to show how the energy density parameters evolve over time in an update of the LightCone7 calculator. See the posts on the thread Steps on the way to Lightcone cosmological calculator. As part of this effort, I ran into some difficulties with deciding how to find and...

Homework Statement Express volume expansivity (B) in terms of density (ρ) and its partial derivatives Homework Equations B = (1/V) (dV/dT) V = m/ρ The Attempt at a Solution I have only managed to substitute m/ρ into the expansivity equation. Don't really understand how to manipulate the...

This question arose in the context of another thread. https://www.physicsforums.com/threads/q-re-article-constraints-on-dark-matter-in-the-solar-system.900573/#post-5669854 Wikipedia gives an estimated value for the DM density near the sun of 0.35 × GeV/cm3 = 6.2 ×10−25 g/cm3. The value of the...

If stars have finite mass, gravity, and density, why does a black hole have infinite density, mass, and gravity and why doesn't it attract everything around it with such infinite gravity? Also, with infinite density, why are black holes all different sizes?

Homework Statement If air has a density of ρ0 on the surface, calculate its density as a function of the height y for two scenarios: (a) the temperature is constant at T0; (b) the temperature decreases linearly T(y) = T0 − ay. Express your results using the given variables together the...

I created interpolative curvefits to the graph of Earth's density as a function of radius, shown here: (Image from Wikipedia) Earth is assumed to be a sphere of radius 6371 kilometers. The independent variable r is the geocentric distance as a fraction of the Earth's radius; i.e. the range of...

From the second Friedmann equation, $$H^2 = \frac{1}{3M_p^2} \rho \quad (k=0, flat)$$ In warm inflation, radiation is present all the way therefore not requiring proper reheating process, so $$\rho = \rho_\phi + \rho_r \, ; \quad \rho_\phi = inflaton, \, \rho_r = radiation$$ But, $$\rho =...

Homework Statement Homework Equations dp/dz=-ρg p=ρgh The Attempt at a Solution I've found the density at depth 3m using ρ=ρ0+kh, which gave me 1060kgm-3. I then put this value into ρgh to get 31195.8Pa which seems to be ≈+1000 off the answer. What is the correct mathematical way of...

I have two questions about the use of stochastic differential equation and probability density function in physics, especially in statistical mechanics. a) I wonder if stochastic differential equation and PDF is an approximation to the actual random process or is it a law like Newton's second...

If you have a density matrix \rho, there is a basis |\psi_j\rangle such that \rho is diagonal in that basis. What are the conditions on \rho such that the basis that diagonalizes it is unique? It's easy enough to work out the answer in the simplest case, of a two-dimensional basis: Then \rho...

follow up from responses in old thread. https://www.physicsforums.com/threads/why-does-attenuation-coefficient-decrease-with-increased-energy.569981/ I have seen in my experiment using a saline media ( some oxygen bubbles) that an increase in Incident PFD is showing an slight increase in the...

If the normalized probability density of the normal distribution is ## p(x) = \frac {1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} ##, then if ##\sigma = 0.0001## and in the special case ## x = \mu##, wouldn't the probability density at this point, ##p(\mu)##, exceed 1 since it is equal...

Hello I've got confused about some features of noise. 1)Can use noise a generator? Well , if we have a noisy resistor and Ideal resistor why can't we use noise voltage according to noise voltage Vn=\sqrt(4KTBR) 2)why we divide power spectral density to RL( load) when we find power at RL?(it is...

Homework Statement Assume that the beaker is half filled with Hg, the steel ball being lighter will float in it half-submerged. Now we pour water into the beaker, so that the beaker is completely filled with water on top, Hg in the bottom and steel ball floating between them. Now my question...

I need to take a look at some references about QFT at finite density but I can't find anything, or at least I don't know where to look. I should emphasize that what I need is QFT at zero temperature and finite density so it seems to me QFT in finite temperature books may not be what I need or...

Homework Statement Example 5.3 from The Marion Thornton book (fifth edition) of Classical Dynamics states the following problem: Consider a thin uniform circular ring of radius a and mass M. A mass m is placed in the plane of the ring. Find a position of equilibrium and determine whether it...

White dwarfs are about the size of the Earth but they are 200,000 to 400,000 times more dense. (They contain almost as much mass as the sun.) Question one: can we duplicate this density in a lab? If so, when did we accomplish that? Matter normally comes in five forms; the common 3 are...

Homework Statement [/B] An unpolarized ruby laser operated at 0.7 μm is projected vertically into a clear sky to investigate the density of the atmosphere. A detector located 10 km from the base of the laser is used to receive the flux density scattered from the laser beam by air molecules...

I am totally confused. What is concerning the anisotropy the difference between re-entering gravity waves and re-entering density perturbations and more important for me what is then happening in the photon-baryon plasma between end of inflation and these re-enterings.

Homework Statement Find magnetic flux density B circulation in closed contour. The countour consists of square with a perimeter of 4b. It includes a square conductor with a perimeter of 4a. A homogenic current flows through a conductor with a current density of j. Homework Equations...

Homework Statement In pyrrole the electron density is maximum on which carbon atom? so if the numbering starts from nitrogen, the carbon on the right side of nitrogen let it be numbered as 2 and the next one as 3 and so on... which of the following options will have the carbons of maximum...

EDIT: Sorry. It's FFT - Fast Fourier Transform, not FTT. I am interested in doing some amateur radio astronomy. Mainly at 1420MHz, hydrogen line. I have a RTL SDR stick. For those who don't know what that is, it's USB DVB-T receiver that can receive anything between 24 – 1766 MHz. Now, there...

Homework Statement Tasks to do: a.)give voltage b.)give the absolute value of charge density for plates Presumably the absolute values of charge densities for plates is equal between the two of them. An electron is accelerated in a homogenic electric field, inbetween two oppositely charged...

Homework Statement A barrel contains 0.130-m layer of oil floating on water that is 0.290 m deep. The density of the oil is 610 kg/m3 What is the gauge pressure at the bottom of the barrel? Homework Equations P [/B]= ρ(g)(h) The Attempt at a Solution I found the pressure of the oil which...

Hi all, This is a followup to a question I asked a number of years ago about the Unruh effect. I understand that an accelerated observer will see warm gas of particles following a blackbody distribution with some temperature T, where as an inertial observer would see none. My question is: how...

I'm reading this paper. But I haven't read anything on how to calculate the density operator in a QFT or how to calculate its trace. Now I can't follow this part of the paper. Can anyone clarify? Thanks

Homework Statement Consider an ensemble of spin 1 systems (a mixed state made of the spin 1 system). The density matrix is now a 3x3 matrix. How many independent parameters are needed to characterize the density matrix? What must we know in addition to Sx, Sy and Sz to characterize the mixed...

Homework Statement [/B] Volume charge density in some space is given by a function ##ρ_v(x)=-ρ_0\frac{x}{a}e^{\frac{-x^2}{a^2}}## where ##ρ_0, a## are positive constants. Determine the electric field vector in arbitrarily chosen point in space. Homework Equations 3. The Attempt at a Solution...

Homework Statement Calculate the electric energy density at the surface of a 3.4 mm diameter copper wire carrying a 28 A current. Homework Equations u = (1/2) ε0 E2 The Attempt at a Solution With the electric energy density equation, I substituted in the equation for the electric field for an...

Homework Statement Calculate the single-particle density of states ##g(\epsilon)## for the dispersion relation ##\epsilon(k) = ak^{\frac{3}{2}}## in 3D. Use ##g(k) = \frac{Vk^2}{2\pi^2}##. Homework EquationsThe Attempt at a Solution This question is worth lots of marks. My solution is a few...

Homework Statement A long rope with mass m = 10 kg is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope and the pulse travels up the rope. (a) Explain why the speed of the wave pulse change as it moves up the rope; does it increase or...

Homework Statement An oscillator is attached to one end of a horizontal string. The other end passes over a frictionless pulley and is held taught by a mass m. The distance between the oscillator and the pulley is 1.2m. The string has a linear mass density of 1.6g/m and the frequency of the...

1. Homework Statement : Homework Equations :[/B] A conductor is an equipotential surface. The charge density near a conductor is proportional to the electric field. Electric field is the negative gradient of potential and thus electric field is in a direction normal to the surface.The Attempt...