How Fast Do Electrons Move in a Copper Wire?

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SUMMARY

The discussion focuses on calculating the charge free to move in a one-meter length of a copper wire with a diameter of 1 mm and a density of 8.47 × 1028 atoms/m3. Additionally, it addresses the drift velocity of electrons when a current of 1 A flows through the wire. The key to solving these problems lies in determining the number of free electrons per copper atom and applying the concept of drift velocity as outlined in the Wikipedia article on drift velocity derivation.

PREREQUISITES
  • Copper atomic structure and free electron theory
  • Basic principles of electric current and charge
  • Understanding of drift velocity in conductors
  • Familiarity with the formula for calculating charge density
NEXT STEPS
  • Calculate the number of free electrons in a copper wire using its atomic density
  • Learn about the formula for drift velocity and its application in conductive materials
  • Explore the relationship between current, charge, and drift velocity
  • Review the derivation of drift velocity as detailed on Wikipedia
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Students and professionals in physics and electrical engineering, particularly those studying electromagnetism and the behavior of electrons in conductive materials.

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1. A copper wire has a diameter of 1 [mm]. The density of the copper atoms inside the wire is 8.47 × 1028 [atoms/m3]. What is the charge that is free to move in a one-meter length of wire?

2. Assume that a current of 1 [A] is flowing from left to right through the wire in the above
problem. How fast are the electrons moving from right to left, in meters per second? (Hint:
consider how much charge has moved past a given point, from right to left, in one second.



Hello, I got these 2 problems left unresolved. I can't figure out how to do them. Don't find an equation that might satisfy these 2 problems. Any help is appreciated!
 
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XodoX said:
1. A copper wire has a diameter of 1 [mm]. The density of the copper atoms inside the wire is 8.47 × 1028 [atoms/m3]. What is the charge that is free to move in a one-meter length of wire?

2. Assume that a current of 1 [A] is flowing from left to right through the wire in the above
problem. How fast are the electrons moving from right to left, in meters per second? (Hint:
consider how much charge has moved past a given point, from right to left, in one second.


Hello, I got these 2 problems left unresolved. I can't figure out how to do them. Don't find an equation that might satisfy these 2 problems. Any help is appreciated!

In 1) they tell you how to find the number of copper atoms. Then if you know how many free electrons there are you might be in business.

In 2) then if you know the number of carriers (copper atoms) then maybe this will help?
http://en.wikipedia.org/wiki/Drift_velocity#Derivation
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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