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A conductor wire having 1029 free electrons / m3 carries a current of 20A. If the cross-section of the wire is 1 mm2, then the drift velocity of electrons will be _______ (e = 1.6 × 10-19 C).
1. 1.25 × 10-4 ms-1
2. 1.25 × 10-3 ms-1
3. 1.25 × 105 ms-1
4. 6.25 × 10-3 ms-1

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Correct Answer - Option 2 : 1.25 × 10-3 ms-1

Concept:

Drift velocity: In a material due to an electric field, The average velocity attained by charged particles.

When electrons are subjected to an electric field they move randomly, then they slowly drift in one direction, in the direction of the electric field applied.

The drift velocity of the electrons is calculated by:

\(v=\frac{I}{neA}\)

where v is the drift velocity, I is the current in the wire, n is the number density of free electrons in the wire, A is the cross-sectional area of the wire, and e is the charge on one electron.

Calculation:

Given that i = 20A; A = 1 mm2 = 10-6 m2; n =1029 m-3; e = 1.6 × 10-19 C;

The drift velocity of the electrons is calculated by:

\(v=\frac{I}{neA}\)

\(v=\frac{20}{(10^{29})(1.6\times10^{-19})(10^{-6})}\)

= 1.25 x 10-3 m/s

So the correct answer is option 2.

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