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Physics Question on Current electricity

A metallic wire of cross sectional area 4 mm24 \, mm^{2} carries a current of 3.2 A3.2 \, A . If 5×10265 \times 10^{26} charge carriers flow across the wire per unit volume, then their drift velocity in m s−1m \,s^{-1} is

A

11

B

0.10.1

C

0.010.01

D

1010

Answer

0.010.01

Explanation

Solution

Here,
Cross-sectional area of the wire,
A=4 mm2=4×10−6 m2A=4\,mm^{2}=4\times 10^{-6}\,m^{2}
Current flowing through the wire , I=3.2 AI=3.2\,A
Number of charge carriers per unit volume of the wire (number density), n=5×1026 m−3n=5\times 10^{26}\,m^{-3} The drift velocity is
vd=IneA=(3.2A)(5×1026m−3)(1.6×10−19C)(4×10−6m2)v_{d}=\frac{I}{neA}=\frac{\left(3.2 A\right)}{\left(5\times10^{26} m^{-3}\right)\left(1.6\times10^{-19}C\right)\left(4\times10^{-6} m^{2}\right)}
=0.01 m s−1=0.01\,m\, s^{-1}