   Chapter 17, Problem 7P

Chapter
Section
Textbook Problem

A 2.0 × 102-km-long high-voltage transmission line 2.0 cm in diameter carries a steady current of 1.0 × 103 A. If the conductor is copper with a free charge density of 8.5 × 1028 electrons/m3, how many years does it take one electron to travel the full length of the cable?

To determine
The time taken by the electron to travel the full length of cable.

Explanation

Given Info: The transmission line has length 2.0×102km and diameter 2.0cm . It carries steady current 1.0×103A , Free charge density in conductor is 8.5×1028electrons/m3 , The transmission line has length 2.0×102km and diameter 2.0cm It carries steady current 1.0×103A Free charge density in conductor is 8.5×1028electrons/m3 .

Explanation:

Formula to calculate drift velocity of electrons in copper wire is

vd=IneA

• vd is the drift velocity of electron,
• I is the current produced ,
• n free charge density,
• e is the charge of electron,
• A is the area of cross section of wire,

Formula to calculate circular area of cross section of wire is,

A=πd24

• A is the area of cross section,
• d is the diameter of the wire,

Substitute the relation for area of cross section in equation to rewrite vd .

vd=Ine(πd24)

Substitute 1.0×103A for I , 8.5×1028electrons/m3 for n , 1.6×1019C for e , 2.0cm for d, and 3.14 for π in the above equation to find vd .

vd=(1.0×103A)(8.5×1028electronsm3)(1

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