Question

A 3.0 m long copper wire is carrying a current of 3.0 A.How longdoes it take for an electron to drift from one end of the wire to the other ? The cross-sectional area of the wire is 2.0 * 10^-6 m^-2 and the number of conduction electrons in copper is 8.5 * 10^28 m^-2 .

Answer 1

The drift velocity of the electrons is given by

v = I / (neA)

here

I = 3A

n = 8.5 X 10²⁸ m³

A = 2 X 10^-6 m²

and e = 1.6 X 10^-19 C

so,

v = 3 / (8.5 X 10²⁸ X 2 X 10^-6 X 1.6 X 10^-19)

or

by solving, we get

v = 1.1 X 10^-4 m/s

Now, to calculate the time taken by the electrons, we simple use the velocity-distance relation, thus,

time = distance / velocity

or t = length of the wire / drift speed

so,

t = 3 / 1.1 X 10^-4

thus, the time taken is, t = 27200 s = 7.55 hrs.