Question

When current is flowing in an ordinary metal wire, the magnitude of the average velocity of the electrons is closest toa) 10 m/sb) the speed of lightc) 10 microns/sd) 1 km/se) 1 m/s

Answer 1

c) 10 microns/s

Step-by-step explanation:

The drift velocity (the velocity of the current) of the electrons in a wire is given by

`v=(I)/(nAq)`

where

I is the current

n is the electron number density (the number of electrons per unit volume)

A is the cross-sectional area of the wire

`q=1.6\cdot 10^(-19) C` is the charge of one electron

Taking a current of

I = 1 A

in a wire of radius r = 1 mm (0.001 m), so with cross-sectional area

`A=\pi r^2 = \pi (0.001 m)^2=3.14\cdot 10^(-6) m^2`

made of copper, whose electron density number is around

`n=8.5\cdot 10^(28) m^(-3)`

we find

`v=(1 A)/((8.5\cdot 10^(28) m^(-3))(3.14\cdot 10^(-6) m^2)(1.6\cdot 10^(-19) C))=2.34\cdot 10^(-5) m/s`

which means that the closest estimate is

c) 10 microns/s