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Q.

A straight copper-wire of length l = 1000 m and cross-sectional area A = 1.0 mm² carries a current i = 4.5 A. The sum of electric forces acting on all free electrons in the given wire is M×10⁶N. Find M. Free electron density and resistivity of copper are 8.5×10²⁸/m³ and $1.7 \times 10^{- 8} Ω$ respectively

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Detailed Solution

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F = NEe [ N = total number of electrons, E = electric field]
$\begin{array}{l} = (nAl) \frac{V}{l} e = nA (IR) e = (nAIe) \frac{ρl}{A} = nIeρl \\ = 8 .5 \times 10^{28} \times 4 .5 \times 1 .6 \times 10^{- 19} \times \\ 1 .7 \times 10^{- 8} \times 1000 = 10^{6} N; M = 1 \end{array}$

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A straight copper-wire of length l = 1000 m and cross-sectional area A = 1.0 mm2 carries a current i = 4.5 A. The sum of electric forces acting on all free electrons in the given wire is M×106N. Find M. Free electron density and resistivity of copper are 8.5×1028/m3 and1.7×10−8Ω respectively