Question

A straight section of silver wire has a cross sectional area A=2.0 mm2. A total of 9.4×1018 electrons pass through the wire in 3.0s. The conduction electron density in silver is 5.8×1028 electrons/m3. How far along the straight section do the electrons in the wire move, on average, during the 3.0s in question?

Answer 1

8.08 x 10^-5 m

Step-by-step explanation:

A = 2 mm^2 = 2 x 10^-6 m^2

Total number of electrons, N = 9.4 x 10^18

time, t = 3 s

n = 5.8 x 10^28 electrons/ m^3

Current, i = Q / t = N x e / t = (9.4 x 10^18 x 1.6 x 10^-19) / 3 = 0.5 A

Let vd be the drift velocity.

i = n e A vd

0.5 = 5.8 x 10^28 x 1.6 x 10^-19 x 2 x 10^-6 x vd

vd = 2.7 x 10^-5 m/s

Distance traveled by the electrons = velocity x time

= vd x t = 2.7 x 10^-5 x 3 = 8.08 x 10^-5 m