What is Energy density: Definition and 201 Discussions

In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It may also be used for energy per unit mass, though a more accurate term for this is specific energy (or gravimetric energy density).
Often only the useful or extractable energy is measured, which is to say that inaccessible energy (such as rest mass energy) is ignored. In cosmological and other general relativistic contexts, however, the energy densities considered are those that correspond to the elements of the stress–energy tensor and therefore do include mass energy as well as energy densities associated with the pressures described in the next paragraph.
Energy per unit volume has the same physical units as pressure, and in many circumstances is a synonym: for example, the energy density of a magnetic field may be expressed as (and behaves as) a physical pressure, and the energy required to compress a compressed gas a little more may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume. A pressure gradient has the potential to perform work on the surroundings by converting internal energy to work until equilibrium is reached.

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  1. boomdoom

    Kinetic energy density in a string (derivative)

    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...
  2. Arman777

    Spherical Shell-Potential Energy, Energy density

    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.
  3. binbagsss

    I How do we measure energy density of radiation?

    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...
  4. O

    I Calculation of negative energy density in a Casimir cavity

    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!
  5. Jorrie

    I Evolution of the Energy Density Parameters

    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...
  6. S

    I Different forms of energy density in inflation

    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 =...
  7. O

    How Do You Calculate Electric Energy Density Near a Copper Wire?

    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...
  8. J

    Electric Field Energy Density: Plates of Q & A

    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...
  9. Spinnor

    B Energy density of charged capacitor via QFT

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

    Derive energy density proportional to emitted power per unit area

    The following derives the relation that for a blackbody radiation the energy density is proportional to the energy emitted per unit area over unit time. The average energy density ##d\psi## is obtained by dividing the radiant energy ##dE## received by the surface ##dB## in 1 second by the...
  11. W

    I Vacuum energy density after inflation

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  12. L

    Traveling EM waves with fixed energy density

    Hi, I'm taking an undergrad course in Electromagnetism and Optics, and in the lecture notes it reads: "Consider the formal equation ε0D⋅E = 1 ... that must be obeyed for waves traveling in different directions as defined by the wave vector k but with a given energy density." Could anyone help me...
  13. C

    A Free energy density in liquid crystals

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  14. Ranku

    I Will a Slow Decrease in Dark Energy Density Alter the Fate of the Universe?

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  15. James William

    I Energy density of a 1D string?

    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...
  16. J

    Negative Energy Density in EM Waves?

    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...
  17. P

    How Do You Calculate Magnetic Energy Density at an Atom's Center?

    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...
  18. xSpartanCx

    Average Energy Density of Capacitor

    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...
  19. T

    Light if energy density of photons were constant

    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 =...
  20. T

    Hubble lookback time based on energy density.

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  21. D

    Wave Energy Density: Discrepancy in Units

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  22. K

    Scalar field energy density and pressure in hot universe

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  23. Quarlep

    Casimir Effect and Calculate Energy Density of it

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  24. acdurbin953

    Thermal energy density of the milky way

    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...
  25. Quarlep

    How is Dark Energy Density Calculated in the Universe?

    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...
  26. wabbit

    Why "Dark Energy density" instead of CC?

    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...
  27. A

    Understanding the Spectral Energy of the Vacuum: A Scientific Exploration

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  28. davidbenari

    E=cB and electromagnetic energy density

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  29. genxium

    Problem on Energy Density in Dielectric Medium

    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...
  30. 2

    Help with deriving the Casimir Effect?

    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...
  31. D

    Calculating energy density in the early Universe

    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...
  32. schrodingerscat11

    Time-average energy density

    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...
  33. schrodingerscat11

    Solving an Electromagnetic Wave Problem

    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...
  34. Helios

    Zero-point energy density evaluation

    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...
  35. D

    On the origin of gravity. (Mass, or energy density?)

    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...
  36. J

    Energy density of the cosmological constant units question

    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...
  37. O

    Proof of Energy Density in Capacitor?

    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...
  38. B

    Energy density of a capacitor

    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...
  39. S

    Energy Density of Blackbody Radiation

    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...
  40. Spinnor

    E&M energy density near a radiating hi Q half-wave antenna.

    A high Q antenna basically means the antenna stores a large amount of energy in the near fields compared with the electromagnetic energy radiated per cycle? When the alternating current momentarily stops in our half-wave antenna charge density is maximum at the ends of the antenna, and the...
  41. H

    Is the energy density normalized differently in the quantum case?

    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...
  42. D

    Pressure, energy density, and power of a fluid flow

    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...
  43. M

    Energy density of magnetic field in a solenoid

    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...
  44. P

    What is the energy density of the electric 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...
  45. P

    What is the energy density of the electric field ?

    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?
  46. D

    Magnetic Field Energy Density Confusion

    I am trying to find the approximate force imparted on a piece of iron on the axis of a finite length solenoid. One website said a good approximation was to take the difference of the magnetic field energy from when the piece of iron was directly outside the solenoid and when the piece of iron...
  47. marcus

    How to derive dark energy density from Jorrie's Hubble radius limit

    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...
  48. H

    Find total momentum as function of energy density

    Homework Statement So here's the question: The momentum flux dP from an infinitesimal monochromatic energy field dE is given by: dP = I/c cos^2θdΩ, where dΩ = sinθdθd∅ Assuming the field is isotropic, find the total momentum P as a function of the energy density u=4πI/c Homework Equations...
  49. S

    Why supercapacitor energy density is so high?

    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...
  50. B

    Energy density and range calculation Electric Vehicle

    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...
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