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a 5.2×10−4 v/mv/m electric field creates a 3.6×1017 electrons/selectrons/s current in a 2.0-mmmm-diameter aluminum wire.

User Dabloons
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1 Answer

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The drift velocity of the electron is determined as 2.15 x 10⁻³ m/s.

How to calculate the drift velocity?

The drift velocity of the electron is calculated by applying the following formula as shown below.

v = I / nAe

where;

  • I is the current
  • A is the area
  • e is the charge of the electron
  • n is the charge density

The area of the wire is calculated as follows.

A = πr²

A = π ( 1 x 10⁻³)²

A = 3.14 x 10⁻⁶ m²

The charge density if calculated as follows;

n = N / V

n = N/AD

n = ( 3.6 x 10¹⁷ ) / ( 3.14 x 10⁻⁶ x 2 x 10⁻³)

n = 5.73 x 10²⁵ A/m³

The resistance of the wire;

R = ρL/A

where;

  • ρ is resistivity of aluminum wire = 2.63 x 10⁻⁸ Ω m

R = (2.63 x 10⁻⁸ x L ) / (3.14 x 10⁻⁶ )

R = 8.38 x 10⁻³ L (Ω/m)

The current flowing in the wire is calculated as;

I = V/R

where;

  • V is the electric potential

V = E × L

I = (E × L) / R

I = (5.2 x 10⁻⁴ x L ) / (8.38 x 10⁻³ L )

I = 0.062 A

The drift velocity of the electron is calculated as;

v = I / nAe

v = (0.062) / (5.73 x 10²⁵ x 3.14 x 10⁻⁶ x 1.6 x 10⁻¹⁹)

v = 2.15 x 10⁻³ m/s

The complete question is below:

a 5.2×10−4 v/mv/m electric field creates a 3.6×1017 electrons/electrons/s current in a 2.0-mmmm-diameter aluminum wire. find the drift velocity of the electron.

User Atanu
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