Question

Consider a wire of length 4 m and cross-sectional area 1 mm2 carrying a current of 2 A. If each cubic metre of the material contains 1029 free electrons, find the average time taken by an electron to cross the length of the wire.

Answer 1

first of all, find drift velocity.

i=neAv_di=neAvd

where, i is current, n is number of electrons per m³ , A is cross sectional area of wire and vd is drift velocity.

so, vd = i/neA

here, i = 2A, n = 10^29 electrons per m³, e = 1.6 × 10^-19C and A = 1mm² = 10^-6 m²

so, vd = 2/(10^29 × 1.6 × 10^-19 × 10^-6)

= 2/(1.6 × 10⁴)

= 1/8000

time taken to cross the length of wire, t = l/vd

where, l is length of wire i.e., l = 4m

so, t = 4/(1/8000) = 32000 sec = 3.2 × 10⁴ sec

hence, 3.2 × 10⁴ sec time taken by an electron to cross the length of wire.