Find the drift speed of electrons in a wire

In summary, we need to find each variable. I is already given to us as 8 amps. The charge of an electron is 1.6 x 10^-19 coulombs. The cross sectional area will just be \pi(1.2\times10^−3)^2\ m^2. Now we need to find the free electron density. We are given the density of copper and can use dimensional analysis to find free electron density. Assume one free electron per copper atom:\frac{8.92g}{cm^3} \times \frac{1 mol}{63.55g} \times \frac{6.022 \times 10^{23}atoms}{1
  • #1
Jaccobtw
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Homework Statement
A cylindrical copper wire has a radius of 1.2∗10^−3 m. It carries a constant current of 8.00A. What is the drift speed of the electrons in the wire in m/s? Assume each copper atom contributes one free electron to the current. The density of copper is 8.92g/cm^3.
.
Relevant Equations
$$v_d = \frac{I}{neA}$$
We need to find each variable. ##I## is already given to us as 8 amps. The charge of an electron is 1.6 x 10^-19 coulombs. The cross sectional area will just be ##\pi(1.2∗10^−3)^2## m^2. Now we need to find the free electron density. We are given the density of of copper and can use dimensional analysis to find free electron density. Assume one free electron per copper atom:

$$\frac{8.92g}{cm^3} \times \frac{1 mol}{63.55g} \times \frac{6.022 \times 10^{23}atoms}{1mol} \times \frac{1 electron}{1 atom} = 8.45 \times 10^{22} \frac{electrons}{cm^3}$$

Plug in numbers

$$\frac{8.0 amps}{(\frac{8.45 \times10^{22}electrons}{cm^3})(1.6\times10^{-19}C)(\pi(1.2\times10^{-3})^2)}$$

I git 130.8 m/s but it was wrong. Can anyone help me find out why?
 
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  • #2
Jaccobtw said:
We are given the density of of copper and can use dimensional analysis to find free electron density.
As much as I love dimensional analysis, it can never give you an exact relation. You can use it to check your answers and deduct the functional form of physical relations up to constants.

Also, 1.2e-3 m is not the same as 1.2e-3 cm.
 
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  • #3
Jaccobtw said:
Homework Statement:: A cylindrical copper wire has a radius of 1.2∗10^−3 m. It carries a constant current of 8.00A. What is the drift speed of the electrons in the wire in m/s? Assume each copper atom contributes one free electron to the current. The density of copper is 8.92g/cm^3.
.
Relevant Equations:: $$v_d = \frac{I}{neA}$$

We need to find each variable. ##I## is already given to us as 8 amps. The charge of an electron is 1.6 x 10^-19 coulombs. The cross sectional area will just be ##\pi(1.2∗10^−3)^2## m^2. Now we need to find the free electron density. We are given the density of of copper and can use dimensional analysis to find free electron density. Assume one free electron per copper atom:

$$\frac{8.92g}{cm^3} \times \frac{1 mol}{63.55g} \times \frac{6.022 \times 10^{23}atoms}{1mol} \times \frac{1 electron}{1 atom} = 8.45 \times 10^{22} \frac{electrons}{cm^3}$$

Plug in numbers

$$\frac{8.0 amps}{(\frac{8.45 \times10^{22}electrons}{cm^3})(1.6\times10^{-19}C)(\pi(1.2\times10^{-3})^2)}$$

I git 130.8 m/s but it was wrong. Can anyone help me find out why?
Carefully simplify the units in your answer. You have some mismatched units which don't "cancel" .
 

FAQ: Find the drift speed of electrons in a wire

1. What is drift speed of electrons in a wire?

The drift speed of electrons in a wire is the average velocity at which electrons move through a wire when a current is applied. It is typically measured in meters per second.

2. How is drift speed of electrons calculated?

The drift speed of electrons can be calculated by dividing the current (in amperes) by the cross-sectional area of the wire (in square meters) and the number of electrons per unit volume (in cubic meters). This is known as the drift velocity formula.

3. What factors affect the drift speed of electrons in a wire?

The drift speed of electrons is affected by the material of the wire, the temperature, and the strength of the applied electric field. It is also influenced by the density and mobility of the electrons in the wire.

4. How does the drift speed of electrons relate to electric current?

The drift speed of electrons is directly proportional to the electric current in a wire. This means that as the current increases, the drift speed of electrons also increases.

5. Why is the drift speed of electrons in a wire relatively slow?

The drift speed of electrons in a wire is relatively slow because electrons are constantly colliding with atoms and other electrons in the wire, which slows down their movement. Additionally, the electric field in a wire is typically weak, further limiting the speed at which electrons can move.

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