How to Calculate the Volume Charge Density of Earth's Atmosphere?

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Homework Help Overview

The discussion revolves around calculating the volume charge density of Earth's atmosphere based on electric field measurements at different altitudes. The problem involves concepts from electrostatics, specifically relating to Gauss's law and electric fields.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the formula for electric field due to a point charge but expresses confusion about the relevance of two different electric field measurements at varying altitudes. Some participants suggest that Gauss's law is essential for solving the problem, while others question the clarity of the equations provided by the instructor.

Discussion Status

Participants are exploring the application of Gauss's law to the problem, with some expressing frustration over the lack of guidance on using the equations provided. There is acknowledgment of a potential misunderstanding regarding the volume calculation in relation to the problem context.

Contextual Notes

There is mention of neglecting the curvature of Earth, which may indicate assumptions about the uniformity of the electric field in the specified region. The original poster also notes a lack of clarity in the problem setup and the equations provided by the professor.

pyroknife
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Homework Statement


In a particular region of Earth's atmosphere, the electric field above Earth's surface has been measured to be 147 N/C downward at an altitude of 260 m and 165 N/C downward at an altitude of 410 m. Calculate the volume charge density of the atmosphere, assuming it to be uniform between 260 and 410 m. (Hint: You may neglect the curvature of Earth. Why?)

Homework Equations


volume charge density = Q/V

I tried doing E=kq/r^2 for the 147 N/C and 260m altitude. -147=(9*10^9)(q)/(260)^2_ and got -0.0011 C. I divided that by volume (4/3*pi*260^3) which gave me -1.5e-11, but that wasn't right.I really have no idea how to even start this. Why did they give me 2 sets of altitude and E field?
 
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Are you learning Gauss's law?
 
yes, our prof just gave us like 20 different equations and never showed us how to use a single one.
 
pyroknife said:
yes, our prof just gave us like 20 different equations and never showed us how to use a single one.

Ouch! I think this problem calls for Gauss' Law which you will want to learn forward and backwards. Then do every relevant problem in your text that has answers so you make sure you understand it. The following sketch might help and if there are mistakes I hope they are pointed out.
 

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it worked thanks. But how come Volume=150A, isn't volume (4/3)*pi*r^3 which would be 150(1/3)*A?
 

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