A copper wire has a circular cross section with a radius of 3.75 mm.

If the wire carries a current of 4.00 A, find the drift speed of the electrons in the wire. (Assume the density of charge carriers (electrons) in a copper wire is n = 8.46 *10^28 electrons/m^3.)

thanks

21

To find the drift speed of the electrons in the wire, you can use the formula:

v = I / (n * A * q)

where:
v = drift speed of electrons
I = current (in amperes)
n = density of charge carriers (in electrons per unit volume)
A = cross-sectional area of the wire (in square meters)
q = charge of an electron (in coulombs)

In this case, the current is given as 4.00 A, and the density of charge carriers in a copper wire is given as n = 8.46 * 10^28 electrons/m^3. The cross-sectional area of the wire can be calculated using the radius.

The formula for the area of a circle is A = π * r^2.

First, convert the radius from millimeters to meters:
radius = 3.75 mm = 3.75 * 10^(-3) m

Now, calculate the cross-sectional area of the wire:
A = π * (3.75 * 10^(-3))^2 = π * 1.40625 * 10^(-5) m^2

Next, substitute the given values into the formula:
v = 4.00 A / (8.46 * 10^28 electrons/m^3 * π * 1.40625 * 10^(-5) m^2 * 1.6 * 10^(-19) C)

Simplify the expression:
v = 4.00 / (8.46 * π * 1.40625 * 1.6) * 10^(-5-19-28) m/s

Calculate the value of v using a calculator, considering the significant figures in the given values, and round the answer to an appropriate number of significant figures.

This will give you the drift speed of the electrons in the copper wire.