Energy density Definition and 186 Threads

is there any way to derive p=rho/3 from 4 vector or stress-energy tensor?

Is the energy density ##\rho## in the early universe and the Hubble scale ##H## during inflation related by the formula $$H^{4} = \frac{9}{64\pi^{2}} \frac{\rho^{2}}{M_{P}^{4}}?$$ Here, ##M_{P}## is the Planck mass. Can you suggest any resources where this is explained?

Homework Statement In our physics course, we were studying one dimensional waves in a string. There, our teacher stated that the kinetic energy in a small piece of a string is dK=\frac{1}{2}μdx\frac{\partial y}{\partial t}^2 were μ is the linear density of the string, so he claimed that...

Homework Statement Homework EquationsThe Attempt at a Solution I fount these Part(a)its ##E=\frac {ρa^3} {3ε_0}## and ##υ=\frac 1 2ε_0E^2## Part (b) ##dU=4πr^2drυ## Part (c) ##U=\int_0^a 4πr^2udr## but it gives me ##U=\frac {-Q^2} {8πε_0a}## This"-" bothers me.

I have that the energy density of matter approx 0.3 , so this is measured by galaxy motion / gravitational lensing etc, that's fine. I have that the energy density due to the vacuum is 0.7, so this is measured by the expansion rate- the common suspect being dark energy. I have radiation...

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!

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...

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 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 Two large non-conducting plates of surface area A=.025m^2 carry equal but opposite charges Q = 75microC. What is the energy density of the electric field between the two plates. Homework Equations I wrote the equations on my attempt. This was a multiple choice problem...

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

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...

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?

Hello, As I understand there is a problem in physics where point-like massive (or charged, etc.) particles would have infinite mass/energy (or charge, etc.) density. I'm curious how in the context of String Theory how we address the same problem? I have come to understand Strings as...

Homework Statement The problem I have is that we are asked to show the complex relative permittivity of a good conductor is erc = 1 + i(sigma)/(omega*epsilon_0) where sigma is the conductivity and omega is the frequency of an electromagnetic wave in the medium. This is fine, I calculated it...

Homework Statement In an atom: suppose one electron orbits the n proton nucleus at radius r . Find the magnetic energy density, in J/m3, at the center of the atom due to the motion of this electron. NOTE: You can ignore the effect of other electrons in this atom. Homework Equations...

Homework Statement An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 48 mm and 72 mm. The electric potential of the inner conductor with respect to the outer conductor is -536 V (k = 1/4πε0 = 8.99 × 109 N · m2/C2) The average energy...

Homework Statement At what rate would stars have to be producing light (how many photons per second per solar mass start) in order for the energy density of photons in the universe be constant? Assume current values of cosmological parameters. Do it for current time. Homework Equations e =...

Homework Statement If the energy density of the vacuum were the value 10^133 eV/m^3 , what would the value of the Hubble lookback time be for such a universe with no curvature and no other matter? Homework Equations Possible equation... ...Lookback time = ln(1+z)/H The Attempt at a Solution...

Homework Statement In deep water, it can be shown that ##\omega = \sqrt{gk/2}## Orcas (killer whales) have been filmed generating waves in deep water to knock seals off ice floes. Assume that an orca can generate a wavepacket which is simply half a sine wave (i.e. ##\sin(kx)## from ##kx =0##...

Kolb&Turner in "the early universe" mentioned that for a scalar field ##\phi## at finite temperature, ##p=-V_T(\phi)## and ##\rho=-p+T\frac{d p(T)}{d T}## where ##V_T## is potential energy including temperature correction. My question is: when we consider the evolution of the universe using...

All we know that space creates particle pairs,virtual particles,they make a pressure and we call it casimir effect.I want to ask in universe Is there such a way to calculate How many particles created per volume per second.Or calculate energy density ? Thanks

Homework Statement Interstellar medium is composed of atomic hydrogen at 100 K and number density 2E-7 m-3. Compute the average thermal energy density of the milky way disk. Then find the average magnetic energy density given the magnetic field strength of 3E-10 T. Homework Equations E=3/2 kT...

Physical cosmology and astronomy, dark energy is an unknown form of energy which permeates all of space and tends toaccelerate the expansion of the universe. Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an...

Not worrying about the term DE exactly - my question really is, why is the CC described as an energy density, instead of just a nonlocal quantity ? Why bother with a constant scalar field when a constant would do ? After all we do not hear talk of a local gravitational strength density which...

Hello, I have seen in various places in the literature the expression for the spectral energy of the vacuum, but I don't seem to find a book/article where the derivation of this expression is shown. Also sometimes people state at its dependence on the third power of frequency is the only form...

I have to questions that I can't seem to understand. I've seen in my textbook the relation E=cB being deduced from Faradays law applied to some type of rectangular loop. The problem is this is done with regards to a planar wave. So is this relationship general for all EM waves? If so, how? And...

I'm reading this tutorial and having some difficulty in understanding its derivation. I take as granted that electric energy within a volume \Omega is defined by: W = \int_\Omega \phi \cdot \rho \cdot d^3r where \phi = \phi(\textbf{r}) is the eletric potential, \rho = \rho(\textbf{r}) is the...

I am at the very last part of a relatively long derivation of the Casimir effect, and I just don't understand the final step D: So far, I have derived the ground state energy to be \langle 0| \hat{H} |0\rangle = \delta (0) \int _{-\infty}^{\infty} dp \frac{1}{2} E And for a massless field...

Homework Statement I've been told to calculate the energy density in the early Universe. It states that it is completely dominated by neutrinos (3 species), photons, electrons, and positrons. Homework EquationsThe Attempt at a Solution Now, I've found an equation to calculate the energy...

Homework Statement Given the energy density expression from Jackson \frac{1}{2}\big(\mathbf{E}\cdot\mathbf{D}+\mathbf{H}\cdot\mathbf{B}\big) (Eq. 6.106) Show the missing steps to arrive at the time-averaged energy density...

Homework Statement For an electromagnetic wave with an electric field given by \mathbf{B}=\mathbf{i} E_o cos (kz-\omega t)+ \mathbf{j} E_o sin (\omega t - kz) where Eo is a constant Find (a) its direction of propagation (b) the magnetic field (c) Poynting vector (d) energy density, i.e., the...

Dear cosmology people, What is a theoretical value for the zero-point energy density of the vacuum? It must be hard to know or even controversial. Even though the zero point field is a QFT topic, the question seems to be cosmological, because only the cosmologist seem to be forthcoming on the...

So I have been reading about the nature of gravity, and I have become a little confused as to how gravity is produced. In some videos and books, they state that it is the mass of an object that generates gravity. However, others say that it's not so much as mass, but the density of energy/mass...

Hi Everyone! I need a bit of help with the following question please. How does the energy density of the cosmological constant Uλ=ρλc^2 have the required SI units if λ=4∏Gρ/c^2 I know that the energy density of the cosmological constant (Uλ)is essentially dark energy and the SI units...

Hi, I just registered and don't know if I opened the post in right place, this is not a homework question, only something I wonder. I know that electric field energy density in a parallel-plate capacitor is; u= ε * (E^2) / 2 and I know how this formula derivated for parallel-plate...

Homework Statement A parallel-plate capacitor with C = 16 mu or micro FF is charged so as to contain 1.7 J of energy. If the capacitor has a vacuum between plates that are spaced by 0.35 mm, what is the energy density (the energy per unit volume)? I am a little lost of this problem and...

Homework Statement \mbox{Let} \ p(< \nu_{0}) \mbox{be the total energy density of blackbody radiation in all frequencies less than} \ \nu_{0}, \mbox{where} \ h \nu_{0} << kT. \mbox{Derive an expression for} \ p (< \nu_{0})Homework Equations p(v) dv = \dfrac{8 \pi h} {c^3} \dfrac...

Hi all, This is all in the context of interaction between (two-level) atoms and an electromagnetic field, basically the Wigner-Weisskopf model. In particular, I tried to derive the value of the atom-field interaction constant and show that it satisfied...

I've read that you can view static pressure of a fluid as energy density, which makes sense to me. I've also seen that the power of a fluid flow can be calculated by multiplying the pressure by the volumetric flow rate. However, doesn't a flow also have kinetic energy? How can you calculate the...

Homework Statement A solenoid that is 117 cm long has a cross-sectional area of 20.0 cm2. There are 1010 turns of wire carrying a current of 9.56 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field...

Two large non-conducting plates of surface area A = 0.25 m^2 carry equal but opposite charges Q = 75 uC. What is the energy density of the electric field between the two plates? My attempt: E=(charge density)/epsilon And U=1/2*epsilon*E^2 So U=0.5(charge density)^2/epsilon...

Two large non-conducting plates of surface area A= 0.25m^2 carry equal but opposite charges Q=75uC. What is the energy density of the electric field between the two plates?

How to derive "dark energy" density from Jorrie's Hubble radius limit (c^4/(8 pi G))*3*(17.3e9 light years)^(-2) Paste that in the google window, and see what you get. When I paste that into google I get 0.5393 nanopascal, which is equivalent to 0.5393 nanojoule per cubic meter. If the...

In battery we have (in ideal) case one electron per atom or three elecrons (in case of aluminum) which flow from anode to cathode.In activaded carbon there should be immensely smaller amount of free electrons than in metals.I do not have exact date for carbon, but for example in Germanium it is...

I want to calculate the range of an Electric Vehicle (EV) with a Li-ion battery of 200 Wh/kg. Parameters v= 50 km/h = 14 m/s A= 0.8 m2 d = 500 m efficiency = η= 85% mc = 900 kg incl. 100 kg battery ρ = 1.3 kg/m3 First I have calculated the power of the EV with a speed of 50 km/h and...

Homework Statement The energy density (energy per unit area per unit time) arriving from the sun at the surface of the Earth is 1300 J/m2s. Calculate the mass loss of the sun in one year. (The Earth is about 1.49 x 1011 m from the sun.) Homework Equations ΔE = Δmc2 KE = (γ-1)mc2 The...

Homework Statement Suppose a laser produces a pulse of light with duration 1 ns, a diameter of 1 cm, and a total energy of 1 mJ. In free space, the pulse length is this 30 cm, the energy density is 42 J/m3, and the irradiance is 1.3*1010 W/m2. Calculate the length, energy density, and...

I understand how the Planck length (1.6 x E-33 cm) is calculated from the equation ,Gh/( 2πc3), but how is the Planck density calculated at E-5 gm/Planck volume (E93 to E94 gm/cm3). It is based on "energy jitters". Also, is there an explanation for the vast difference between the observed...

Homework Statement How do I calculate the energy density of either a main-spring (like in a clock) or a motor-spring? Can someone show me values put into the correct formula for something like e.g. steel? I did find some material properties like this...