Estimating Earth's Atmospheric Electrical Energy Potential: A Calculation Guide

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In summary, the conversation is about estimating the electrical energy stored in Earth's atmosphere, as energy prospectors from a distant planet are considering stealing it. The solution involves using the Earth's electric field and treating the atmosphere as a flat slab. After some calculations and discussions with the TA, it is determined that the volume used in the equation should be the surface area of the Earth multiplied by the thickness of the slab.
  • #1
fball558
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Earths potential?

Homework Statement



the problem reads as folloed
Energy prospectors from a distant planet are inspecting the Earth to decide if its electrical energy resources are worth stealing. Measurements reveal that Earth's electric field extends upward for 800 m and has an average magnitude of 190 V/m. Estimate the electrical energy stored in the atmosphere.

our TA gave us a hint and said
You may treat the atmosphere as a flat slab with an area equal to the surface area of the earth.



The Attempt at a Solution



i tried to derive an equation. i keep getting the wrong answer so please check my math and see if I am doing it wrong or just some calculation error.

i started with
U=1/2 Eo * E^2 Eo is 8.85e^-12
then i went to
U=EV substitued V=4/3pir^3 so got
U=E4/3pi*r^3
this is where i got stuck. i asked my TA and he said i was doing good so far.
i played around with some stuff and got my U (potential) as follows
U=E4pi*r^2*d
but i get the wrong answer. any help would be great ;)
thanks
 
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  • #2


fball558 said:
our TA gave us a hint and said
You may treat the atmosphere as a flat slab with an area equal to the surface area of the earth.

You're using the wrong volume, it's not a solid sphere.

What is the surface area of the Earth?
What is the volume of a slab that has that area, and the thickness given in the problem statement?
 
  • #3


I would approach this problem by first clarifying that Earth's potential is not a measurable quantity, as potential is a relative concept and requires a reference point. However, we can estimate the electrical energy stored in the atmosphere based on the given information.

To calculate the electrical energy stored in the atmosphere, we can use the formula:

Energy = 1/2 * ε0 * E^2 * A

Where ε0 is the permittivity of free space, E is the electric field strength, and A is the surface area of Earth.

Using the given values of E = 190 V/m and A = 4πr^2 (where r is the radius of Earth), we can estimate the energy stored in the atmosphere as:

Energy = 1/2 * 8.85e^-12 * (190)^2 * 4πr^2
= 1.27 x 10^14 J

This is a significant amount of energy, and it is important for us to consider how this energy is naturally balanced and maintained in the Earth's atmosphere. Additionally, we can also consider how this energy can be harnessed and utilized for various purposes, such as renewable energy sources.
 

1. What is the purpose of calculating Earth's atmospheric electrical energy potential?

The purpose of calculating Earth's atmospheric electrical energy potential is to determine the amount of energy that can potentially be harnessed from the Earth's atmosphere. This can help in the development of renewable energy sources and understanding the power potential of our planet's atmosphere.

2. How is Earth's atmospheric electrical energy potential calculated?

The calculation of Earth's atmospheric electrical energy potential involves taking into account several factors such as the Earth's surface area, the electric field strength, and the atmospheric conductivity. These variables are used in a mathematical formula to estimate the total energy potential of the atmosphere.

3. Can the energy potential of the atmosphere be harnessed for practical use?

Yes, the energy potential of the atmosphere can be harnessed for practical use. However, the technology to do so is still in its early stages and requires further development. One example of harnessing atmospheric electrical energy is through the use of lightning rods and lightning harvesting systems.

4. Are there any limitations to calculating Earth's atmospheric electrical energy potential?

Yes, there are limitations to calculating Earth's atmospheric electrical energy potential. The calculation is based on several assumptions and simplifications, and the actual energy potential may vary depending on different environmental factors. Additionally, the technology to harness this energy is still in its early stages and may not be able to fully utilize the estimated potential.

5. What are some potential applications of harnessing Earth's atmospheric electrical energy?

Some potential applications of harnessing Earth's atmospheric electrical energy include powering remote areas, supplementing traditional power sources, and reducing dependence on fossil fuels. Additionally, this energy can also be used for communication and weather monitoring systems.

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