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
To find the drift speed of electrons in the wire, we can use the formula:
v_d = I / (n * A * q)
where:
v_d is the drift speed of electrons,
I is the current flowing through the wire,
n is the density of charge carriers (electrons) in the wire,
A is the cross-sectional area of the wire, and
q is the charge of an electron.
Let's calculate the drift speed step by step:
1. Convert the radius from millimeters to meters:
radius = 3.75 mm = 3.75 * 10^(-3) m
2. Calculate the cross-sectional area of the wire:
A = π * radius^2
3. Obtain the charge of an electron:
q = 1.6 * 10^(-19) C (coulombs)
4. Substitute the given values into the formula:
v_d = 4.00 A / (8.46 * 10^28 electrons/m^3 * π * (3.75 * 10^(-3) m)^2 * 1.6 * 10^(-19) C)
5. Simplify the expression and calculate the result:
v_d = (4.00 * 10^0 A) / (8.46 * 10^28 electrons/m^3 * 3.14159 * (3.75 * 10^(-3) m)^2 * 1.6 * 10^(-19) C)
v_d ≈ 1.85 * 10^(-4) m/s
Therefore, the drift speed of the electrons in the copper wire is approximately 1.85 * 10^(-4) m/s.