Density Definition and 1000 Threads

Homework Statement Find the total charge Q given the charge density ρ(r)=ε0A(4πδ3(r)-π2e-λr/r The Attempt at a Solution I know the solution's steps start with: Q=∫ρdr=ε0A(4π∫δ3(r)dr-λ2∫e-λr(4πr2)/rdr) What I don't understand is where that 4πr at the end comes from. That last step is only...

Homework Statement This isn't really a problem I've been given, but questions i have about how the author of my textbook, Leon Couch, Digital and Analog communications Systems, found the PSD (power spectral density) of an digital NRZ pulse train. Homework Equations The PSD of a periodic signal...

Hello all, I have been arguing about this for a few days. My friend is telling me that a helicopter flies in the air because there is a difference in density on top of the propeller and below the propeller.The air on top of the helicopter has less density and the bottom has more density. This...

Hello everyone, I have a physics problem that I have been struggling with for a long time. Many many hours of searching around for theoretical or practical answers have not given me anything definitive. The question is in the context of electrical engineering, more specifically peaks in...

I was watching a lecture in which the professor derived the Navier Stokes Equations for const density and viscosity. He however skipped a step and directly went from one equation to another without giving any explanation. I have attached an image file in which the 2nd equation is derived from...

Hello all, Is there any direct relation ship exists between the thermal expansion and density of polymer material (eg. PMMA, Teflon) ? Like, Lorentz- lorentz law relates directly the refractive index and density of the polymer. similarly any laws relating (thermal expansion and density of...

Electromagnetic field has a density of energy U = ε/2*E2+ μ/2* H2 And a density of momentum, given by the Poynting vector S = E x H For an element of volume dV you have a four vector of energy and momentum which is [E,P] = dV * [U, S] Being E the energy in the element of volume and P the...

Hope I'm in the right section for this question! In the big bang model, the expansion of the universe is slowed down by gravity. If there is enough matter in the universe, then the expansion can be overcome and the universe will collapse in the future. The density of matter that is just...

Homework Statement Calculate the surface density (planar density) of the Silicon diamond structure in the [1 0 0],[1 1 0],[1 1 1] planes. Given a = 5.431 A (latice constant) Hint: For the (111) plane, it should help you to think of the diamond lattice as two interpenetrating FCC lattices.2...

In wikipedia says Physical baryon density: ##Ω_bh^2=0.02230±0.00014## and Physical dark matter density:##Ω_ch^2=0.1188±0.0010## Matter density:##Ω_m=0.3089±0.0062## so If we collect baryonic matter density and dark matter density we...

Homework Statement Sakurai Modern Quantum Mechanics Revised Edition. Page 81. density matrix p = 3/4 [1 0; 0 0] + 1/4 [1/2 1/2; 1/2 1/2]. We leave it as an exercise to the reader the task of showing this ensemble can be decomposed in ways other than 3.4.24Homework Equations 3.4.24 w( sz +...

A disk with a uniform positive surface charge density lies in the x-y plane, centered on the origin. The disk contains 2.5 x 10-6 C/m2 of charge, and is 7.5 cm in radius. What is the electric field at z = 15 cm? I have used the formula...

There are two numericals, 1. Density of Methanol is 0.793 kg/l. Find molarity. ANSWER is : Desity/ Molar mass = Molarity (UNDERSTANDABLE) In other numerical 2. Concentration of H2SO4 is 98% by mass having density of 1.84gm/ml. Calculate Molarity. here they used another formula. now my...

Normal density of Earth is 5,5 tons/m3 and surface gravity is 9,8 m/s and. But if we would compress mass of Earth to 50 km diameter, we would get density 1,4 mil tons/m3 and surface gravity would be 158 860 m/s. I know the math, in basic gravity equotation F=Gm1m2/r2 with decreasing r you get...

Hi... I want to know why charge density is higher at sharp points in a conductor? I have gone through the analogy of two spheres connected by a wire... But is there any other explanation which is not specific to spheres...?

Homework Statement Random variable X is uniformly distributed on interval [0,1]: f(x)=\begin{cases} 1 & \text{ if } 0\leq x\leq 1\\ 0 & \text{ else} \end{cases} a) Find probability density function ρ(y) of random variable Y=\sqrt{X} +1 I tried like this. Is it good, if no why not...

Hello. I'm studying principle of Langmuir probe and got several questions. 1st, the textbook suddenly tells that ion density within sheath is ni(x) = nis(Vs/V(x))1/2 where nis, Vs are ion density and plasma potential at sheath edge. I found some document which shows that it is obtained by...

Homework Statement The figure shows a composite slab with dimensions d1 = 11.6 cm, d2 = 2.85 cm, and d3 = 13.4 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are (a) the x coordinate, (b) the y coordinate, and(c) the z...

Hi there guys, I'm conducting an experiment to calculate the mass flow rate of water. Bellow is a copy of the procedure: 1) Weigh the mass in kg of a container 2) Connect a flow meter to a tap (any source) with a pipe and insure the departure pipe goes into a sink 3) Open the tap an increase...

Homework Statement I have to expand the following term: $$\dfrac{1}{4} F_{\mu\nu}F^{\mu\nu} = \dfrac{1}{4} \left(\partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}\right) \left(\partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}\right)$$ to get in the end this form...

What is current density

we know i = dq/qt = enLA/dt = en(Vd)(A) standard derivation i en(Vd)(A) where e is charge on electron n is electrons per unit vol. Vd is drift velocity of electrons A is area of cross section of conductor SO my doubt is if we have a conical conductor or some kind of conductor whose CSA is not...

Homework Statement Three very long (theoretically infinite long) hollow cylindrical conductors, with radius a,b,c (c>b>a) are in vacuum. Inner and central conductor are charged, and outer conductor is grounded. Potentials of inner and central conductors with reference point relative to outer...

Hi All, I have spent hours trying to understand the matrix form of Density Operator. But, I fail. Please see page 2 of the attached file. (from the book "Quantum Mechanics - The Theoretical Minimum" page 199). Most appreciated if someone could enlighten me this. Many thanks in advance. Peter Yu

Is there a solid that has a density of or below the density of air or any gas?

Why can not the density of states of a metal at Fermi level be zero? Thanks!

Surface current density, K is defined as: K = σv where σ is surface charge density and v is velocity. Given a uniformly charged spherical shell with radius R, spinning at constant angular velocity ω, find the current. So, I start with this formula: dI = K dl dI = σ Rω dl and I placed the...

When you look at a viscous fluid its so thick and it seams that its dense and a runny fluid seams less dense. Like if you take a bottle of syrup it fells a bit heavier than a bottle of water. Plus if the atom are packed closer to each other (and in the form of liquid the atoms move past each...

The Purcell effect is when an atom placed inside a high finesse cavity with a very small mode volume gets an increase in the spontaneous emission rate. I've tried to find correct explanation for this effect, but it seems hard to find, except that it comes from an increase in the vacuum density...

Here is a question about probability density. I am trying to work it out using a different method from the method on the textbook. But I get a different answer unfortunately. Can anyone help me out? Question: Let X be uniformly distributed random variable in the internal [ 0, 1]. Find the...

I'm picturing a comoving particle, meaning at rest with respect to CMB? Does expansion affect the probability density, density current? I can't see how it wouldn't? But then it seems like there would have to be a uniform negative probability density current everywhere.

I have one question. Charge density waves are usually defined as phase transitions on metal in which electrons started to behave like collective. Is this happen always in quasi one dimensional metals? Also why this transition actually happens?

I was searching a cosmology calculator and In one calculator I saw this equation. ##1=Ω_k+Ω_m+Ω_Λ## is that true true for all type universe's (open,flat,closed) ? and is here ##Ω_k={-k\over H^2_0 /a^2_0}## isn't it. (And If you can give me an article about this issue I will be...

Homework Statement I came across a recent problem that asked me to calculate the flux density at the end of a solenoid. I was given the current 3 A , the number of turns per unit length , 12 cm-1 and the using the permeability of free space as 4π × 10^-7 Homework Equations The equation I used...

A spherical shell has an outside radius of 2.75 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.59 g/cm3. The space inside the shell is filled with a liquid having a density of 1.00 g/cm3. (a) Find the mass m of the sphere, including...

The density of an object equals its mass divided by its volume. The mass of Earth is 6x10e+24 and its radius is 4000 miles (1.61km = 1mile). What is the density of the Earth in kg/m^3?V=4/3pi(r)^3. D=M/VConverting 4000 to Km, I get 6400. After plugging it into the Volume equation, I end up with...

Dear all, In his book chapter " Green’s Function Methods for Phonon Transport Through Nano-Contacts", Mingo arrives at the Green's function for the end atom of a one dimensional lattice chain (each atom modeled as a mass connected to neighbouring atoms through springs). He gives the green...

I need to measure the density of aqueous microdroplets in oil. My first idea was to obtain a set volume of the droplet-in-oil mixture and weigh it to obtain the density, weigh the same volume of oil without droplets, then estimate the volume of the droplets so I can work out their density...

Homework Statement A cylinder of radius a and length l has charge distribution ρ=Cr2 where C is a constant and r is radial distance in cylindrical coordinates. Derive an expression for the average charge density within the cylinder. Homework Equations Well, charge density given is within the...

1. The problem statement, all variables and given/known data Show that the probability density as a function of seperation, r, of two atoms interacting via a potential U(r) (e.g. a function of separation only, such as a Coulombic interaction), is given by $$\rho(r) = Cr^2e^{-\beta U(r)}$$...

Homework Statement If an object is 500 N normally but has an apparent weight of 300 N when submerged in water, what is the density of the object? Homework Equations ρobjVobjg = ρfluidVobjg The Attempt at a Solution So the correct answer is 2500 kg/m3 but when I set up the problem, it doesn't...

The question seems to be of quite low level yet many of teachers i found are unable to explain me the exact concept that what is mass density and volume.Yeah i know the formula d=m/v also v=a^3... Please explain what practically & exactly they are and how both formula has came exactly. Please...

Good afternoon all, I'm investigating typical values of entropy for a subsystem of a 1D (non-interacting) spin chain. Most of the problem is essentially solved I've shown that a typical pure state of the entire chain is close (trace norm) to the state ##\Omega_S## when reduced. \Omega_S =...

Dear PF Forum, I have a question about the size of "singularity" This question has already been asked here, Question about Schwarzschild radius But what I want to know is this density thing that I'd like a confirmation. Actually it's 2.9511896078372906 KM according to his...

The GHZ state is: |\psi> = \frac{|000> + |111>}{\sqrt2} To calculate density matrix we go from: GHZ = \frac{1}{2}(|000> + |111>)(<000| + <111|) GHZ = \frac{1}{2}( |000><000| + |111><111| + |111><000| + |000><111|) To: GHZ = 1/2[ \left( \begin{array}{cc} 1 & 0 & 0 & 0 & 0 &...

If we connect a two metals with different Fermi levels electrons will start to flow from metal with higher Fermi level to a lower one. Untill metal with lower Fermi level will get negatively charged and the process will stop. But what if we connect a two materials with different Fermi levels...

I want to know Universe density according to this equation( ##k=-1##) ? ##H^2(t)-8πρG/3=-k/a^2(t)## ##ρ_U=ρ_m+p_r## ##ρ_U##=Universe density ##ρ_m##=Matter density ##p_r##=Radiation density

Homework Statement Homework Equations PV=nRT The Attempt at a Solution not sure if this is the right approach plugging into -ρg gives us -PMg/RT = dP/dy now we have to integrate both sides to find P?

Since the flow of heat in solids happens due to the collision of the molecules with each other, thereby increasing their internal energy, a higher denser material will have molecules closer, does it mean that the thermal conductivity of high density materials will be higher than the lower...

I want to ask if it is wrong to interpret the von Neumann density in a '' functional sense'' as a szego projector Hilbert spaces? thks