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Calculate the energy density of the Earth's atmosphere 
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#1
Mar1712, 09:44 AM

P: 4

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. 


#2
Mar1712, 01:41 PM

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hi phystudent515!
i find the question very confusing also the answer … energy density isn't in J, it's in Pa (pascals) have you given us the whole question? 


#3
Mar1712, 05:48 PM

P: 4

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): 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. 


#4
Mar1912, 05:22 AM

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Calculate the energy density of the Earth's atmosphere
hi phystudent515!
yes, that second 4.4 is clearly a misprint … the typesetter has got bored and typed the number twice! 1/2 B^{2}/µ_{o} is the correct formula btw, J/m^{3} and Pa are the same, see eg http://en.wikipedia.org/wiki/Energy_...Energy_density … 


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