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The number density of free electrons in ...

The number density of free electrons in a copper conductor is estimated at `8.5 xx 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? The area of cross-section of the wire is `2.0 xx 10^(-6)m^(2)` and it is carrying a current of 3.0A.

Text Solution

Verified by Experts

The drift velocity of electrons through a conductor is given by:
`v_(d) = (I)/(n eA)`
Here, `n= 8.5 xx 10^(28) m^(-3)`
`A = 2 xx 10^(-6) m^(2), I= 3.0A`
`v_(d) =(3)/(8.5 xx 10^(28) xx 1.6 xx 10^(-19) xx 2 xx 10^(-6))`
If length of the conductor, l=3m, let t be the time taken by an electron to drift from one end of the wire to its other end.
`:. v_(d) = (3)/(t) = (3)/(8.5 xx 10^(28) xx 1.6 xx 10^(-19) xx 2 xx 10^(-6))`
`rArr t= 8.5 xx 11^(28) xx 1.6 xx 10^(-19) xx 2 xx 10^(-6)`
`rArr t= 27.2 xx 10^(3) s= 7.5` hours
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