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Question
The number density of free electrons in a copper conductor is 8.5 × 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 × 10−6 m2 and it is carrying a current of 3.0 A.
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Solution
Given: Number density of free electrons in a copper conductor, n = 8.5 × 1028 m−3
Length of the copper wire, l = 3.0 m
Area of cross-section of the wire, A = 2.0 × 10−6 m2
Current carried by the wire, I = 3.0 A, which is given by the relation,
Formula: I = nAeVd
Where,
e = Electric charge = 1.6 × 10−19 C
Vd = Drift velocity =`"Length of the wire (l)"/"Time taken to cover l(t)"`
I = `(nAel)/t`
t = `(nAel)/I`
= `(3 xx 8.5 xx 10^28 xx 2 xx 10^-6 xx 1.6 xx 10^-19)/3.0`
= `(81.6 xx 10^3)/3.0`
= 27.2 × 103 s
Therefore, the time it takes for an electron to drift from one end of the wire to the other is 27.2 × 103 s.
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