# Finding the drift speed of a conduction electrons

• Omar FTM
In summary, a wire with diameter 4R and a wire with diameter 2R are connected by a tapered section. The wire is made of copper and carries a current. The electric potential change along the length of 1.95m in section 2 is 13.5 µV. The number of charge carriers per unit volume is 8.49x10^28 m-3. The drift speed of the conduction electrons in section 1 is calculated to be 7.41e-9 m/s, but this answer may be incorrect due to a possible misprint or error in the problem.
Omar FTM

## Homework Statement

The figure shows wire section 1 of diameter 4R and wire section 2 of diameter 2R, connected by a tapered section. The wire is copper and carries a current. Assume that the current is uniformly distributed across any cross-sectional area through the wire's width. The electric potential change V along the length L = 1.95 m shown in section 2 is 13.5 µV. The number of charge carriers per unit volume is 8.49x10^28 m-3. What is the drift speed of the conduction electrons in section 1?

v = j/nq
j=E/p = v/pL

## The Attempt at a Solution

I got J2 using the provided v2 and p ( of copper = 1.72e-8) and the L2
J2 = (13.5e-6)/(1.72e-8)(1.95) = 402.5 A/m^2
Then I used the relation between the two sections > J1A1 = J2A2 >>> J1(0.25Pi 4^2 ) = J2(0.25Pi 2^2) >>> j1 = 100.625 A/m^2
The drift speed of sec 1 would be >>> V1 = J1 / nq = 100.625/(8.49e28)(1.6e-19) = 7.41e-9 m/s ( which was a wrong answer ) what is my mistake ?

Last edited:
I don't see any errors. Be sure that you are using the values for n and ρ from your textbook rather than from the internet. The values could vary a little depending on the source of information.

I double checked my p and n , they are correct ( from the book (copper = 1.72e-8 ) , n from the question itself = 8.49x10^28 ) , but it's still telling me that my answer is wrong :(

I still can't find any error in your calculation. Maybe we're overlooking something that someone else will catch.

Any one ? :)

I am not real familiar with this kind of problem, but the math looked right. I did find an example on Wiki (under "Drift Velocity"), and because of the negative charge of an electron, the result came out to be negative. That's the only possibility I can come up with.

TomHart said:
I am not real familiar with this kind of problem, but the math looked right. I did find an example on Wiki (under "Drift Velocity"), and because of the negative charge of an electron, the result came out to be negative. That's the only possibility I can come up with.
That's a thought. But speed is the magnitude of velocity, so I would think the answer should be positive. Anyway, thanks for the input, Tom.

TSny said:
But speed is the magnitude of velocity
Yep, good point.

Maybe, they meant mV instead of μV. It was a wire almost 2 m long!

ehild said:
Maybe, they meant mV instead of μV. It was a wire almost 2 m long!
Yes, could be. I had noticed the current density and drift speed were coming out very small. For j = 400 A/m2 and a wire of cross-sectional area 0.5 mm2, the current is only 0.20 mA.

I get your point , but this is how the question is :D
I think that I won't be able to solve it ...

TSny said:
Yes, could be. I had noticed the current density and drift speed were coming out very small. For j = 400 A/m2 and a wire of cross-sectional area 0.5 mm2, the current is only 0.20 mA.
Yes, the set-up and data for such a practically usual problem should be "real" , with a common voltage source and voltage measurable with a common voltmeter, multimeter. The smallest range of a common multimeter is 100-200 mV.
@Omar FTM Your solution is correct. It is quite possible that it was a misprint in the text of the problem.

Tried answering using V as mV instead of micro V , still wrong :(

Omar FTM said:
Tried answering using V as mV instead of micro V , still wrong :(
It is also possible that the problem writers made some mistake. It happens quite often.

## 1. How do you find the drift speed of conduction electrons?

To find the drift speed of conduction electrons, you can use the formula I = nAvq, where I is the electric current, n is the number of conduction electrons per unit volume, A is the cross-sectional area of the conductor, v is the drift speed, and q is the charge of the electron. Rearranging this formula, you can solve for v to find the drift speed.

## 2. What is the significance of calculating the drift speed of conduction electrons?

Calculating the drift speed of conduction electrons is important because it helps us understand the flow of electric current in a conductor. This information can be used to design and improve electrical circuits and devices.

## 3. How does temperature affect the drift speed of conduction electrons?

As temperature increases, the drift speed of conduction electrons also increases. This is because higher temperatures cause more collisions between the electrons and the atoms in the conductor, resulting in a higher average drift speed.

## 4. Can the drift speed of conduction electrons be greater than the speed of light?

No, the drift speed of conduction electrons is typically very slow, usually on the order of millimeters per second. This is much slower than the speed of light, which is approximately 299,792,458 meters per second.

## 5. How does the material of the conductor affect the drift speed of conduction electrons?

The type of material in the conductor can affect the drift speed of conduction electrons. Materials with higher electrical conductivity, such as copper, have a higher number of conduction electrons and therefore a higher drift speed compared to materials with lower conductivity, such as rubber.

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