A small but measurable current of 3.20 E-10 A. exists in a copper wire whose diameter is 0.03 cm. Calculate the electron drift speed (in meters/second).

Question

A small but measurable current of 3.20 E-10 A. exists in a copper wire whose diameter is 0.03 cm. Calculate the electron drift speed (in meters/second).

Answer 1

You will need to first calculate the number density of free conducting electrons. Call it N. It equals the number density of copper atoms. You can get that from the density of copper and the atomic weight.

For the drift velocity V, use the equation

N*e*V*A= 3.2*10^-10 coulombs/second

A is the cross sectional area, pi*D^2/4

Answer 2

ive previously tried this and obtained 3.34e-13 m/s which the computer says is wrong

where N = 8.46e28 m^-3
e = 1.6e-19 C
and A = 7.07e-8 m^2

Answer 3

Let's see if I agree with your value of N.

Copper density = 8.92 g/cm^3
Copper atomic weight = 63.5 g/mole
Copper molar density = 0.1405 mole/cm^3
= 1.405*10^5 moles/m^3
= 8.456*10^28 atom/m^3
That equals the free electron number density, N

A = (pi/4)*(3*10^-4 m)^2 = 7.06*10^-8 m^2

V = 3.35*10^-13 m/s

I agree with your number.

Answer 4

To calculate the electron drift speed, we need to use the formula:

𝑉(𝑑𝑟𝑖𝑓𝑡) = 𝐼/(𝑛𝑒𝐴𝑞)

Where:
𝑉(𝑑𝑟𝑖𝑓𝑡) is the electron drift speed
𝐼 is the current in Amperes
𝑛𝑒 is the number of electrons per unit volume in the wire
𝐴 is the cross-sectional area of the wire
𝑞 is the charge of an electron

Let's break down the information provided:
𝐼 = 3.20 E-10 A (current)
𝑑 = 0.03 cm (diameter)
𝑟 = 𝑑/2 = 0.015 cm (radius)

To find the cross-sectional area 𝐴 of the wire, we can use the formula:

𝐴 = 𝜋𝑟^2

𝜋 is a mathematical constant (approximately 3.14).

Let's substitute the values and calculate 𝐴:

𝐴 = 3.14 * (0.015 cm)^2
𝐴 = 0.007065 cm^2

Now, we need to convert the area to square meters:

1 cm^2 = (1/100)^2 m^2
𝐴 = 0.007065 * (1/100)^2 m^2
𝐴 = 7.065 E-7 m^2

Next, we'll find the number of electrons per unit volume (𝑛𝑒). For copper, the number of conduction electrons per unit volume is approximately 8.5 E28 electrons per cubic meter.

Now, we can substitute the values into the formula:

𝑉(𝑑𝑟𝑖𝑓𝑡) = 3.20 E-10 A / (8.5 E28 electrons/m^3 * 7.065 E-7 m^2 * 1.6 E-19 C)

Simplifying further:

𝑉(𝑑𝑟𝑖𝑓𝑡) = 3.20 E-10 A / (8.5 E28 * 7.065 E-7 * 1.6 E-19 m^5/C)

Calculating the value:

𝑉(𝑑𝑟𝑖𝑓𝑡) ≈ 0.2755 m/s

Therefore, the electron drift speed in the copper wire is approximately 0.2755 meters/second.