Question

A copper wire has a square cross section 2.0 mm on a side. The wire is 5.0 m long and carries a current of 2.0 A. The density of free electrons is 8.5*1028/m3. How much time is required for an electron to travel the length of the wire?

Answer 1

30.22 hours

Step-by-step explanation:

Given data:

A= l² = (2 x
`10^(-3)`)² = 4 x
`10^(-6)` m²

Length 'L' = 5m

current '
`I`' = 2 A

density of free electrons 'n'= 8.5 x
`10^(28)` /m³

Current Density 'J' =
`I`/ A

J= 2/4 x
`10^(-6)`

J= 5 x
`10^(5)` A/m²

We can determine the time required for an electron to travel the length of the wire by

T= L/ Vd

Where,

L is length and Vd is drift velocity.

Vd can be defined by J/ n|q|

where,

n is the charge-carrier number density

|q| is is the charge carried by each charge carrier =>1.6 x
`10^(-19)`C

T= L/ Vd

Therefore,

T= L . n|q| / J

T= (4 x 8.5 x
`10^(28)` x |1.6 x
`10^(-19)`|)/5 x
`10^(5)`

T= 108800 seconds =>1813.33 minutes

Converting minute into hours:

T= 30.22 hours

Thus, time that is required for an electron to travel the length of the wire is 30.22 hours