Question

A length of wire has a radius of 3.00 × 10-3 m and a resistance of 0.200 Ω. When the potential difference across the wire is 10.0 V, the electron drift speed is found to be 2.98 × 10-4 m/s. On the basis of these data, calculate the density of free electrons in the wire.

Your help is much appreciated! :)

Answer 1

Compute the current I using Ohm's law.

The flux of free electrons F is the free electron density tomes the drift velocity v. If you multiply this flux by the electron charge and the cross section, you get the current. By equating this with what you get from Ohm's law, you can thus solve for the free electron density.

Answer 2

Call the free electron density N, m^-3
e = electron charge , Coulombs
V = electron drift speed
I = current, Amps
A = cross sectional area, pi r^2, m^2

I = N*A*e*V

Solve for N in this case.
Get the current I from ohms law. I = V/R