The drift velocity of the electron is determined as 2.15 x 10⁻³ m/s.
How to calculate the drift velocity?
The drift velocity of the electron is calculated by applying the following formula as shown below.
v = I / nAe
where;
- I is the current
- A is the area
- e is the charge of the electron
- n is the charge density
The area of the wire is calculated as follows.
A = πr²
A = π ( 1 x 10⁻³)²
A = 3.14 x 10⁻⁶ m²
The charge density if calculated as follows;
n = N / V
n = N/AD
n = ( 3.6 x 10¹⁷ ) / ( 3.14 x 10⁻⁶ x 2 x 10⁻³)
n = 5.73 x 10²⁵ A/m³
The resistance of the wire;
R = ρL/A
where;
- ρ is resistivity of aluminum wire = 2.63 x 10⁻⁸ Ω m
R = (2.63 x 10⁻⁸ x L ) / (3.14 x 10⁻⁶ )
R = 8.38 x 10⁻³ L (Ω/m)
The current flowing in the wire is calculated as;
I = V/R
where;
- V is the electric potential
V = E × L
I = (E × L) / R
I = (5.2 x 10⁻⁴ x L ) / (8.38 x 10⁻³ L )
I = 0.062 A
The drift velocity of the electron is calculated as;
v = I / nAe
v = (0.062) / (5.73 x 10²⁵ x 3.14 x 10⁻⁶ x 1.6 x 10⁻¹⁹)
v = 2.15 x 10⁻³ m/s
The complete question is below:
a 5.2×10−4 v/mv/m electric field creates a 3.6×1017 electrons/electrons/s current in a 2.0-mmmm-diameter aluminum wire. find the drift velocity of the electron.