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A potential difference of 100 V is applied to the ends of a copper wire one meter long. What is the average drift velocity of electrons ? (given $σ = 5.81 \times 10^{7} Ω^{- 1} m^{- 1}, n_{c u} = 8.5 \times 10^{28} m^{- 3})$

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0.43 $m s^{- 1}$

0.83 $m s^{- 1}$

0.52 $m s^{- 1}$

0.95 $m s^{- 1}$

answer is A.

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Detailed Solution

$V = n e V_{d} ρ l$

Since $ΔV = 100 V, l = 1 m$ .

$∴ electric field = \frac{ΔV}{1} = \frac{100}{1} = 100 {Vm}^{- 1}$

Also conductivity $σ = 5.81 \times 10^{7} Ω^{- 1} m^{- 1}$

$\begin{array}{l} n = 8.5 \times 10^{28} m^{- 3} \\ ∴ v_{d} = \frac{σ}{en} E = \frac{5.81 \times 10^{7} \times 100}{1.6 \times 10^{- 19} \times 8.5 \times 10^{28}} = 0.43 m s^{- 1} \end{array}$

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