Question

A length of metal wire has a radius of 0.003 m and a resistance of 0.1 ω. when the potential difference across the wire is 16 v, the electron drift speed is found to be 0.000282 m/s. based on these data, calculate the density of free electron in the wire. the fundamental charge is 1.6 × 10−19
c. answer in units of m−3 .

Answer 1

By definition;
Vd = I/nQA

In which,
Vd = drift speed = 0.000282 m/s
I = current through the wire = V/R = 16/0.1 = 160 Amps
n = Density of free electrons
Q = Fundamental charge = 1.6*10^-19 C
A = Cross-sectional area of the wire = πr^2 =π*0.003^2 = 2.827*10^-5 m^2

Rearranging the expression for Vd above and substituting;
n = I/VdQA = 160/(0.000282*1.6*10^-19*2.827*10^-5) = 1.254*10^29 free electrons/m^3