Question

A copper conductor has a number density of free electrons estimated of 8.5 10 28 m 3. The area of the cross-section of the wire is 2.010 6 m 2 and it is carrying a current of 3.0

a. Find the drift velocity. How long does an electron take to drift from one end of a wire 3.0 m long to its other end?

Answer 1

Calculate the drift velocity Vd=IneAVd=IneA

Given n=85×1028/m3n=85×1028/m3

A=2×10−6m2A=2×10−6m2

I=3AI=3A

e=1.6×10−7Ce=1.6×10−7C

Time taken by electron to drift from one end to continue of the wire,

t=length of the wiredrift velocityt=length of the wiredrift velocity

=lVd

Use the relation ,

I=neAVdI=neAVd

=> Vd=IneAVd=IneA

t=lneAIt=lneAI

substituting the values we get,

t=lneAIt=lneAI

=3×8.5×1028×1.6×10−19×2×10−63=3×8.5×1028×1.6×10−19×2×10−63

∴t=2.72×104S∴t=2.72×104S

==7 hours and minute

The time taken by an electron to drift from one end to another end is 7 hours and 33 mins