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The Number Density of Free Electrons in a Copper Conductor Estimated in Example 3.1 is 8.5 × 10^28 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

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.

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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,

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`

`=(3xx8.5xx10^28xx2xx10^-6xx1.6xx10^-19)/3.0`

`=2.7xx10^4s`

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 Class 12 Physics Textbook
Chapter 3 Current Electricity
Q 13 | Page 128
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