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Physics Question on Electromagnetic induction

What is the drift velocity of electons, if the current flowing through a copper wire of 1 mm1\,mm diameter is 1.1 A1.1\, A ? Assume that each atom of copper contributes on electron (Given, density of Cu=9g cm−3Cu= 9 g \, cm^{-3} and atomic weight of Cu=63Cu = 63)

A

0.3 mm s−10.3\, mm\, s^{-1}

B

0.5 mm s−10.5\, mm\, s^{-1}

C

0.1 mm s−10.1\, mm\, s^{-1}

D

0.2 mm s−10.2\, mm\, s^{-1}

Answer

0.1 mm s−10.1\, mm\, s^{-1}

Explanation

Solution

i=neAvdi=n e A v_{d}
n= Avogadros number  Volume of 63 gof copper n=\frac{\text { Avogadros number }}{\text { Volume of 63 gof copper }}
6.02×102363×10−39×103=6.02×10237cm3\frac{6.02 \times 10^{23}}{\frac{63 \times 10^{-3}}{9 \times 10^{3}}}=\frac{6.02 \times 10^{23}}{7} cm ^{3}
n=6.02×10297m3n=\frac{6.02 \times 10^{29}}{7} m ^{3}
i=neAvdi=n e A v_{d} or vd=ineAv_{d}=\frac{i}{n e A}
=1.1×76.02×1029×1.6×10−19×π×(0.5×10−3)2=\frac{1.1 \times 7}{6.02 \times 10^{29} \times 1.6 \times 10^{-19} \times \pi \times\left(0.5 \times 10^{-3}\right)^{2}}
0.1×10−3ms−10.1 \times 10^{-3} ms ^{-1}
=0.1 mm s−1=0.1\, mm\, s ^{-1}