The number density of free electrons in a copper conductor is 8.5 x 10²⁸ m^–3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 x 10^–6 m² and it is carrying a current of 3.0 A.

Solution

Given,
Number density of electrons, n = 8.5 x 10²⁸ m^–3 Current carried by the wire, I = 3.0 A
Area of cross-section of the wire, A = 2.0 x 10^–6 m²Length of the wire, l = 3.0 m
Charge on electron, e = 1.6 x 10^–19 C

Using the formula for Drift velocity $ν_{d} = \frac{I}{neA}$ $= \frac{3}{8.5 \times 10^{28} \times 1.6 \times 10^{- 19} \times 2.0 \times 10^{- 6}} m s^{- 1} = 1.103 \times 10^{- 4} m s^{- 1}$

Therefore,
Time taken by an electron to drift from one end to another end is,
$t = \frac{l}{ν_{d}} = \frac{3.0}{1.103 \times 10^{- 4}} s = 2.72 \times 10^{4} s (\approx 7.5 h) .$

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The number density of free electrons in a copper conductor is 8.5 x 10²⁸ m^–3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 x 10^–6 m² and it is carrying a current of 3.0 A.

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Current Electricity

The number density of free electrons in a copper conductor is 8.5 x 1028 m–3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 x 10–6 m2 and it is carrying a current of 3.0 A.

Some More Questions From Current Electricity Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The number density of free electrons in a copper conductor is 8.5 x 10²⁸ m^–3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 x 10^–6 m² and it is carrying a current of 3.0 A.