1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Calculate the energy density of the Earth's atmosphere

  1. Mar 17, 2012 #1
    Not really homework, just practice for a midterm, I also have the correct answers; but I guess this is the correct section.

    1. The problem statement, all variables and given/known data

    In the Earth's atmosphere we have an electric field with a vertical direction down towards the earth. The lower part of the atmosphere has a typical field strength of 100 V/m. The strength of the earth's magnetic field is approximately 50*10^(-6) T.

    Find the energy density in each of the two layers.

    I assume the "two layers" are the upper and lower layers.

    2. Relevant equations

    [tex] \mbox{Energy density} = \frac{\mbox{Electric energy}}{\mbox{Volume}} = (1/2)\kappa \epsilon_0 E^2[/tex], where k is the Dielectric constant, e_0 is the permittivity of the space (8.85*10^(-12))

    We also have that [tex]\kappa = \frac{E_0}{E}, E = \frac{F}{q_0}[/tex].

    3. The attempt at a solution

    I assume that I could just obtain the energy density directly from using [tex](1/2)\kappa \epsilon_0 E^2[/tex] directly? I know the correct answers should be [tex]u_1 = 4.4\cdot 10^{-8} J, u_2 = 4.4\cdot 10^{-4} J[/tex] However I don't know how to proceed to obtain the variables.
    Last edited: Mar 17, 2012
  2. jcsd
  3. Mar 17, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi phystudent515! :smile:

    i find the question very confusing :redface:

    also the answer … energy density isn't in J, it's in Pa (pascals) :confused:

    have you given us the whole question? ​
  4. Mar 17, 2012 #3
    Forgive me, the unit for the correct answers are [tex]J/m^3[/tex], I simply misread. However I don't know if this seems more correct or not.

    I did omit some text due to it being translated by hand. I'll try to restate the problem text somewhat better worded (due to translation):

    That is the entire problem text with nothing omitted.

    I have tried the following to obtain the same solutions:

    For the electric field: [tex](1/2)\kappa \epsilon_0 E^2[/tex] = 1/2 * 1 * 8.85*10^(-12) * 100^2 = 4.4 * 10^(-8), which is correct.

    For the magnetic field: I use [tex](1/2) \epsilon_0 E^2 + \frac{B^2}{2\mu_0}[/tex] = 1/2 * 8.85*10^(-12) * 100^2 + (50*10^(-6))^2/(2*4*pi*10^(-7)) = 9.94*10^(-4), which is not correct. I observe however that it is roughly twice that of the result I'm looking for.
  5. Mar 19, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    hi phystudent515! :smile:

    yes, that second 4.4 is clearly a misprint …

    the typesetter has got bored and typed the number twice! :zzz:

    1/2 B2o is the correct formula

    btw, J/m3 and Pa are the same, see eg http://en.wikipedia.org/wiki/Energy_densityhttp://en.wikipedia.org/wiki/Energy_density [Broken] …
    Last edited by a moderator: May 5, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook