Calculating Electric Potential for an Earth-Cloud Capacitor

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In summary, the capacitance of the parallel-plate capacitor formed by the Earth and a cloud layer 820m above the Earth is 1.37×10-8 F. The maximum charge the cloud can hold is 55.15 C, and the magnitude of the difference in electric potential between the cloud and the ground is 2.22E17 J. The formula used to calculate the electrical potential energy of a system is U = qV, where q is the charge and V is the voltage. Using this formula, the correct answer for the magnitude of the difference in electric potential is 2.22E17 J.
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Boozehound
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this question has three parts. i figured out the first and second one. i just don't understand electrical potential energy.

Consider the Earth and a cloud layer 820m above the Earth to be the plates of a parallel-plate capacitor. If the cloud layer has an area of 1.27 km2 = 1.27E+6 m2, what is the capacitance? 1.37×10-8 F

If an electric field strength greater than 4.91E+6 N/C causes the air to break down and conduct charge (lightning), what is the maximum charge the cloud can hold? 55.15C

If the cloud is holding this maximum charge, what is the magnitude of the difference in electric potential between the cloud and the ground?

i took the V the i found in the second problem which was 4.026E9V. and i took q from the second problem and multiplied it by V. i ended up getting 2.22E11. which is wrong..what am i doing wrong? i think i might be using the wrong formulas.
 
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The correct answer to the third part of the question is 2.22E17 Joules (J). The formula used to calculate the electrical potential energy of a system is U = qV, where q is the charge and V is the voltage. In this case, q is the maximum charge the cloud can hold (55.15 C) and V is the difference in electric potential between the cloud and the ground (4.026E9 V). Therefore, U = qV = 55.15C * 4.026E9 V = 2.22E17 J.
 
  • #3


As a scientist, it is important to use the correct formulas and units when solving problems. In this case, you are using the correct formula for electric potential energy (U=qV), but you are using the wrong units for the charge (Coulombs) and voltage (Volts). The correct units for charge in this problem are Coloumbs (C) and for voltage, it is Volts/meter (V/m). This is because the electric field strength (E) is measured in N/C or V/m. So, to find the magnitude of the difference in electric potential between the cloud and the ground, you need to use the formula V=Ed, where d is the distance between the cloud and the ground (820m). Therefore, the magnitude of the difference in electric potential between the cloud and the ground is 4.026E9 V/m x 820m = 3.30E12 V. This is a very high potential difference, which explains why lightning occurs when the electric field strength is greater than 4.91E+6 N/C.
 

What is an Earth-Cloud Capacitor?

An Earth-Cloud Capacitor is a hypothetical device that would use atmospheric electricity to create a charge imbalance between the Earth's surface and the clouds. This charge could potentially be harnessed for various purposes, such as generating electricity or controlling weather patterns.

How does an Earth-Cloud Capacitor work?

The exact mechanism of how an Earth-Cloud Capacitor would work is not yet fully understood, as it is still a theoretical concept. However, it is thought that the device would use a combination of conductive materials, such as metal rods, and insulating materials, to create a charge imbalance between the Earth's surface and the clouds.

What are the potential benefits of an Earth-Cloud Capacitor?

If an Earth-Cloud Capacitor could be successfully developed and utilized, it could potentially have several benefits. These could include generating clean and renewable energy, controlling weather patterns to prevent natural disasters, and reducing the negative impacts of lightning strikes on infrastructure.

What are the potential drawbacks of an Earth-Cloud Capacitor?

As with any new technology, there are potential drawbacks and risks associated with an Earth-Cloud Capacitor. These could include potential disruptions to the Earth's natural electric field, unintended consequences on weather patterns, and the need for extensive research and testing before implementation.

Is an Earth-Cloud Capacitor currently being developed or used?

At this time, an Earth-Cloud Capacitor is still a theoretical concept and is not currently being developed or used. However, there is ongoing research and experimentation in this field, and it is possible that the technology could be developed in the future.

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