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A silver wire has a cross sectional area A = 2.0 mm2. A total of 9.4 × 1018 electrons pass through the wire in 3.0 s. The conduction electron density in silver is 5.8 × 1028 electrons/m3 and e = 1.60 × 10-19 C. What is the drift velocity of these electrons? A silver wire has a cross sectional area A = 2.0 mm2. A total of 9.4 × 1018 electrons pass through the wire in 3.0 s. The conduction electron density in silver is 5.8 × 1028 electrons/m3 and e = 1.60 × 10-19 C. What is the drift velocity of these electrons? 1.1 × 10-5 m/s 7.4 × 10-5 m/s 9.1 × 10-5 m/s 5.2 × 10-5 m/s 2.7 × 10-5 m/s

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Answer:

The drift speed of electrons is [tex]2.7 * 10^{-5} m/s[/tex]

Explanation:

We define our Values

Number of electrons [tex](n)= 9.4 * 10^{18} electrons[/tex]

Area [tex]A = 2 mm^2 = 2 * 10^{-6} m^2[/tex]

Time [tex](t) = 3 s[/tex]

[tex]\rho = 5.8*10^{28}electrons/m^3[/tex]

[tex]e= 1.6*10^{-19}c[/tex]

To find the drift velocity we need to use the formula

[tex]v= \frac{I} {N*A*e}[/tex]

However we do not have the current, for that we need the equation,

[tex]I = \frac{n*e}{t}[/tex]

[tex]I=\frac{9.4*10^{18}1.6*10^{-19}}{3}[/tex]

[tex]I = 0.501 A[/tex]

The conduction electron density in silver, [tex]\rho = 5.8*10^{28} electrons/m^3[/tex]

Replacing the previous value of current in Drift Velocity Formula,

[tex]v=\frac{ 0.501}{ 5.8 * 10^28 * 2 * 10^{-6} * 1.6 * 10^{-19}}[/tex]

[tex]v = 2.7 * 10^{-5} m/s[/tex]

We can conclude that the drift speed of electrons is [tex]2.7 * 10^{-5} m/s[/tex]

shubhamchouhanvrVT

The drift speed of electrons will be equal to  

[tex]V= 2.7\times 10^{-5}\ \dfrac{m}{s}[/tex]

What will be the drift velocity of the electron?

The drift velocity is defined as the average velocity of a charged particles like electrons in the material due the influence of the electric field.

The given value in the question,

Number of electrons             [tex]n= 9.4\times 10^{18}[/tex]

Cross section                         [tex]Area = 2\ mm^2=2\times 10^{-6}\ m^2[/tex]

Time taken by electrons       [tex]\rm Time \ t=2\ sec[/tex]

Electron density                     [tex]\rho=5.8\times 10^{28} \ \frac{electron}{m^3}[/tex]

The charge on electron         [tex]e=1.6\times 10^{-19}[/tex]

The formula to calculate the drift velocity will be

[tex]V=\dfrac{I}{\rho\times A\times e}[/tex]

The value of the current will be calculated by the formula.

[tex]I= \dfrac{n\times e}{t}[/tex]

[tex]I= \dfrac{9.4\times 10^{18}\times 16\times 10^{-19}}{3}[/tex]

[tex]I=0.501\ A[/tex]

The conduction electron density in silver,

[tex]\rho=5.8\times 10^{28}\ \frac{electron}{m^3}[/tex]

Now putting the value of the current and density in the formula

[tex]V=\dfrac{I}{\rho\times A\times e}[/tex]

[tex]V=\dfrac{0.501}{5.8\times 10^{28}\times 2\times 10^{-6}\times 1.6\times 10^{-19}}[/tex]

[tex]V=2.7\times 10^{-5}\ \frac{m}{s}[/tex]

Thus the drift speed of electrons will be equal to  

[tex]V= 2.7\times 10^{-5}\ \dfrac{m}{s}[/tex]

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