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Physics Question on Current electricity

At room temperature, copper has free electron density of 8.4 × 1028 m−38.4 \, \times \, 10^{28} \, m^{- 3} . The electron drift velocity in a copper conductor of cross-sectional area 10−6 m210^{- 6} \, m^{2} and carrying a current of 5.4 A5.4 \, A , will be -

A

4 m s−14 \, m \, s^{- 1}

B

0.4 m s−10.4 \, m \, s^{- 1}

C

4 cm s−14 \, c m \, s^{- 1}

D

0.4 mm s−10.4 \, m m \, s^{- 1}

Answer

0.4 mm s−10.4 \, m m \, s^{- 1}

Explanation

Solution

Use i=ne Avdi=ne \, A v_{d} ∴ vd=ineA\therefore \, v_{d}=\frac{i}{n e A} vd=5.48.4×1028×1.6×10−19×10−6v_{d} = \frac{5.4}{8.4 \times 10^{28} \times 1.6 \times 10^{- 19} \times 10^{- 6}} vd=5.4×10−38.4×1.6v_{d} = \frac{5.4 \times 10^{- 3}}{8.4 \times 1.6} vd=0.4  mm  s−1v_{d} = 0.4 \, \, m m \, \, s^{- 1}