When current is flowing in an ordinary metal wire, which is closest to the average drift speed of the electrons?

Option C is correct.

1mm/s

Explanation:

Drift velocity for electrons in wires is the average velocity attained by charged electrons in a material due to an electric field or their average velocity of the electrons during the conduction of electricity.

It is given mathematically as

v = I/(nAq)

where v = drift velocity

I = current in the wire

n = number of electrons per cubic metre for the wire

A = Cross sectional Area of the wire

q = charge on one electron

Electrons normally move with speed close to the speed of light in vacuums but the drift velocity of an electron in conductors is usually very small (mm/s range!).

This is because when electrons move randomly towards higher potential, electrons continuously collide and scatter off of crystal defects, phonons, impurities and vacancies in the conductor in a random fashion. Due to such collisions, electron lose some of their kinetic energy. As a result, electrons do not accelerate but travels with a finite average velocity which we refer to as a drift velocity.

Although as soon as the electric field is established in the conductor, the current starts flowing inside the conductor at the speed of light and not at the speed at which the electrons are drifting.

For example, we will pick common, relatable values for these parameters.

Drift velocity is given mathematically as

v = I/(nAq)

where v = drift velocity

I = current in the wire = assume 10 A

n = number of electrons per cubic metre for the wire = assume the conductor is copper, n = 8.5 × 10²⁸ electrons/m³

A = Cross sectional Area of the wire = assume wire of radius 1mm, A = πr² = 3.142 × 10⁻⁶ m²

q = charge on one electron = 1.602 × 10⁻¹⁹ C

v = (10)/(8.5 × 10²⁸ × 3.142 × 10⁻⁶ × 1.602 × 10⁻¹⁹)

v = 2.34 × 10⁻⁴ m/s = 0.234 mm/s which shows the value is closest to 1 mm/s