The number density of free electrons in a copper conductor estimated in Example 3.1 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? - Physics

Numerical

The number density of free electrons in a copper conductor estimated in Example 3.1 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.

Solution

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,

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 = "nAe""l"/"t"

t = "nAel"/"I"

= (3 xx 8.5 xx 10^28 xx 2 xx 10^-6 xx 1.6 xx 10^-19)/3.0

= 2.7 × 104 s

Therefore, the time taken by an electron to drift from one end of the wire to the other is 2.7 × 104 s.

Concept: Electric Currents in Conductors
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APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 3 Current Electricity
Exercise | Q 3.13 | Page 128
NCERT Class 12 Physics Textbook
Chapter 3 Current Electricity
Exercise | Q 13 | Page 128
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