Question

A 2.9×10^−4 V/m electric field creates a 2.0×10^17 electrons/s current in a 2.0-mm -diameter aluminum wire.

a. What is the drift speed?
b. What is the mean time between collisions for electrons in this wire?

Answer 1

The drift speed in the wire is 0.00748 m/s and the mean time between collisions for electrons in the wire is 3.578 x 10⁻¹⁴ s.

Step-by-step explanation:

To calculate the drift velocity, we can use the formula I = nqAvd, where I is the current, n is the number of free electrons per cubic meter, q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity. In this example, we are given the current and the electric field, so we can calculate A and n using the given diameter of the wire and the density of aluminum. The drift velocity can then be found by rearranging the formula.

To find the mean time between collisions, we can use the formula τ = (m*vd) / (n*q*A), where τ is the mean time between collisions, m is the mass of an electron, vd is the drift velocity, n is the number of free electrons per cubic meter, q is the charge of an electron, and A is the cross-sectional area of the wire.

a. The drift speed is 0.00748 m/s.

b. The mean time between collisions for electrons in this wire is 3.578 x 10⁻¹⁴ s.