Drift velocity and copper wire

In summary, the conversation discusses the calculation of drift velocity and number of conducting electrons in a copper wire based on given dimensions and current. The formula used for drift velocity is v=I/nae and for the number of conducting electrons is n=I/ave. The answer for the number of conducting electrons in 10.0 cm length of the wire is calculated to be 8.0 x 10^-3. The individual asking for help is unsure of how to calculate a, but is advised to refer to the same location where the formula for drift velocity was obtained.
  • #1
hoyy1kolko
10
0

Homework Statement


A copper wire of diameter 2.00mm carries a current of 0.50A.The number of conducting electrons per metre cube of copper is 8.00 x 10^28.
a)Calculate the drift velocity of the conducting electrons.
b)What is the number of conducting electrons in 10.0cm length of the wire


Homework Equations


I=nave
v=I/nae


The Attempt at a Solution


a) I=nave
v=I/nae
= 0.50/(8.00x10^25)(1x10^-3)(1.6x10^-19)
=3.9 x 10^-5 ms^-1
b)I=nave
n=I/ave
=0.50/(1x10^-3)(3.9x10^-5 )(1.6x10^19)
=8.0x 10^-3

The answer that i get is wrong.i don't know why.I need help and explanation.Is it need to derivate the formula then calculate?Thank you.
 
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  • #2
What formula did you use to calculate a?
 
  • #3
i don't know how to calculate a.I need help.
 
  • #4
hoyy1kolko said:
i don't know how to calculate a.I need help.
We help those who help themselves. What does a represent? Look at the same place where you got the equation for the drift velocity.
 
  • #5



The drift velocity of conducting electrons in a copper wire is calculated using the formula v = I/nae, where I is the current, n is the number of conducting electrons per cubic meter, a is the cross-sectional area of the wire, and e is the charge of an electron. In this case, the current is 0.50A, the number of conducting electrons per cubic meter is 8.00 x 10^28, and the cross-sectional area of the wire can be calculated using the diameter of 2.00mm. Therefore, the correct calculation for the drift velocity is:

v = (0.50A)/(8.00 x 10^28)(π(0.001m)^2)(1.6 x 10^-19C)
= 1.98 x 10^-5 ms^-1

For part b), the length of the wire is 10.0cm, which is equal to 0.1m. Therefore, the number of conducting electrons in this length of the wire would be:

n = (0.50A)/(1.98 x 10^-5 ms^-1)(0.1m)(1.6 x 10^-19C)
= 1.26 x 10^24 electrons

It is important to make sure that all units are consistent in the calculations, and to use the correct values for the cross-sectional area and length of the wire. I hope this helps clarify the correct solution for this problem.
 

1. What is drift velocity?

Drift velocity is the average speed at which electrons move through a material when an electric field is applied. It is the result of the random motion of electrons due to thermal energy and the force exerted on them by the electric field.

2. How is drift velocity related to current?

Drift velocity is directly proportional to the current in a material. This means that as the drift velocity of electrons increases, the current also increases.

3. How does the type of material affect the drift velocity?

The type of material can greatly affect the drift velocity. Materials with higher conductivity, such as copper, have a higher drift velocity compared to materials with lower conductivity. This is because materials with higher conductivity have more free electrons available to move in response to an electric field.

4. How does the diameter of the copper wire impact drift velocity?

The diameter of the copper wire has a minimal effect on drift velocity. As long as the wire is large enough to allow for the flow of electrons, the drift velocity will remain relatively constant. However, a thicker wire may have a slightly higher drift velocity compared to a thinner wire due to the presence of more free electrons.

5. Can the drift velocity of electrons in a copper wire be measured?

Yes, the drift velocity of electrons in a copper wire can be measured using various techniques such as the Hall effect or by measuring the resistance of the wire. However, the drift velocity is typically very small (on the order of millimeters per second) and difficult to measure accurately.

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