# A copper wire of 10-2 cm2 has 1029 electrons per m3 of the wire. If the current through the wire is 20 A, the drift velocity is-

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A copper wire of 10-2 cm2 has 1029 electrons per m3 of the wire. If the current through the wire is 20 A, the drift velocity is-
1. 1.25 × 10-3 m/s
2. 1.25 × 10-4 m/s
3. 125 × 10-3 m/s
4. 1.25 × 10-6 m/s

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Correct Answer - Option 1 : 1.25 × 10-3 m/s

The correct answer is option 1) i.e. 1.25 × 10-3 m/s

CONCEPT:

• Drift velocity: The average velocity attained by the electrons under the influence of an electric field is termed the drift velocity
• The free electrons are always in a constant random motion in the conductor.
• When the conductor is connected to a battery, an electric field is generated.
• When these free electrons are subjected to an electric field, they slowly drift in the direction of the electric field applied, while maintaining the random motion.
• At this point, the net velocity of the electrons is called its drift velocity.

The drift velocity (vd) of the electron in a conductor is given by:

$v_d =\frac{I}{nAq}$

Where I is the current flowing through the conductor, A is the area of cross-section of the conductor, q is the charge on the electron and n is the number of electrons.

CALCULATION:

Given that:

Current, I = 20 A

Cross-sectional area of conductor, A = 10-2 cm2 = 10-6 m2

Density of electrons in the wire, n = 1029 electrons per m3

$\Rightarrow v_d= \frac{20}{(10^{29})\;\times\;(10^{-6})\;\times\;(1.6\;\times\;10^{-19})}=1.25 \times 10^{-3}\:m/s$