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Chapter 4: Q12E (page 842)

A copper wire has a square cross-section 2.3 mm on a side. The wire is 4.0 m long and carries a current of 3.6 A. The density of free electrons is8.5脳1028/m3. Find the magnitudes of (a) the current density in the wire and (b) the electric field in the wire. (c) How much time is required for an electron to travel the length of the wire?

Short Answer

Expert verified
  1. Current density in the wire isJ=6.8脳105A/m2
  2. Electric field in the wire isE=11.69脳10-3V/m
  3. Time required by the electron蟿=22.22hr

Step by step solution

01

Step 1:

Given data:

A=l2=2.3脳10-3m2=5.3脳10-6m2L=4.0ml=3.6A

Density of free electrons=8.5脳1028/m3

(a) Current density in the wire is:

J=IA=3.6A5.3脳10-6m2=6.8脳105A/m2

Therefore, the current density in the wire isJ=6.8脳105A/m2.

02

Step 2:

(b) Electric field in the wire is:

As the copper resistivity is蚁=1.72脳10-8惟路m

So electric field is:

E=蚁J=1.72脳10-8惟路m6.8脳105A/m2=0.01169V/m=11.69脳10-3V/m

Hence, the electric field in the wire isE=11.69脳10-3V/m.

03

Step 3:

(c) Time required to travel the length of the wire:

From the equation,

蟿=Lvd

Here vdis drift speed;

vd=Jnq

So, the time required is:

蟿=Lvd=L路nqJ=4.0m脳8.5脳1028脳-1.6脳10-19C6.8脳105A/m2=80000s=1333.33min=22.22hr

Therefore, the time required by the electron蟿=22.22hr.

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