Respuesta :
Answer:
(a). The drift velocity is [tex]2.34\times10^{-5}\ m/s[/tex].
(b). The time is [tex]4.27\times10^{6}\ sec[/tex]
Explanation:
Given that,
Radius = 1 mm
Current = 1 A
Distance = 100 m
(a). We need to calculate the drift speed
Using formula of drift velocity
[tex]v_{d}=\dfrac{i}{neA}[/tex]
Where, i = Current
n = number density
e = charge on electron
A = area cross section
We know that,
The molar mass of copper is 63.55 g/mol.
The mass density is 8.96 g/cm³.
We need to calculate the number of density
[tex]n=\dfrac{\rho}{M}[/tex]
Put the value into the formula
[tex]n=\dfrac{8.96}{63.55}[/tex]
[tex]n=0.141\ mol/cm^3[/tex]
[tex]n=\dfrac{0.141\times6.022\times10^{23}}{10^{-6}}[/tex]
[tex]n=8.49\times10^{28}\ electron/cm^3[/tex]
Put the value into the formula of drift velocity
[tex]v_{d}=\dfrac{1}{8.49\times10^{28}\times1.6\times10^{-19}\times\pi\times(0.001)^2}[/tex]
[tex]v_{d}=0.00002343\ m/s[/tex]
[tex]v_{d}=2.34\times10^{-5}\ m/s[/tex]
(b). We need to calculate the time
Using formula of distance
[tex]t=\dfrac{d}{v}[/tex]
Put the value into the formula
[tex]t=\dfrac{100}{2.34\times10^{-5}}[/tex]
[tex]t=4.27\times10^{6}\ sec[/tex]
Hence, (a). The drift velocity is [tex]2.34\times10^{-5}\ m/s[/tex].
(b). The time is [tex]4.27\times10^{6}\ sec[/tex]
