To calculate the average drift velocity of electrons, we can use the formula:

v = I / (nAq)

where v is the drift velocity, I is the current, n is the number density of electrons, A is the cross-sectional area of the wire, and q is the charge of an electron.

We know that the potential difference applied to the copper wire is 100 V. Therefore, the current flowing through the wire is given by:

I = V / R

where R is the resistance of the wire. Using the formula:

R = ρL / A

where ρ is the resistivity of copper and L is the length of the wire, we can find the resistance of the wire. Using the given values of resistivity, length, and cross-sectional area, we get:

R = (5.81 x 10^7 ohm^-1 m^-1) x (1 m) / (π x (0.5 x 10^-3 m)^2) = 0.031 ohm

Substituting this value in the formula for current, we get:

I = (100 V) / (0.031 ohm) = 3225.81 A

Substituting the given values of number density and charge of an electron, we get:

v = (3225.81 A) / (8.5 x 10^28 m^-3 x π x (0.5 x 10^-3 m)^2 x 1.6 x 10^-19 C) = 0.0074 m/s

Therefore, the average drift velocity of electrons in the copper wire is 0.0074 m/s.



The thermal velocity of electrons is given by:

vth = sqrt((3kT) / (m))

where k is the Boltzmann constant, T is the temperature, and m is the mass of an electron. Using the given temperature of 27 degrees Celsius (300 K) and the mass of an electron, we get:

vth = sqrt((3 x 1.38 x 10^-23 J/K x 300 K) / (9.11 x 10^-31 kg)) = 1.36 x 10^5 m/s

Comparing this value with the average drift velocity calculated above, we see that the thermal velocity is much larger than the drift velocity. This is because the thermal velocity represents the random motion of electrons due to their thermal energy, while the drift velocity represents the net motion of electrons in a particular direction due to the applied electric field. Despite the small drift velocity, the large number of electrons in the wire results in a significant current flowing through the wire.



In this problem, we have calculated the average drift velocity of electrons in a copper wire of length 1 meter and cross-sectional area 1 mm^2, when a potential difference of 100 V is applied to the ends of the wire. We have used the formula v = I / (nAq) to calculate the drift velocity, where I is the current, n is the number density of electrons, A is the cross-sectional area of the wire, and q is the charge of an electron. We have also used the formula R = ρL /