A current of 10 A exists in a wire of cross-sectional area of $5 \mathrm{~mm}^{2}$ with a drift velocity of $2 \times 10^{-3} \mathrm{~ms}^{-1}$. The number of free electrons in each cubic meter of the wire is:

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Current Electricity

A current of 10 A exists in a wire of cross-sectional area of

5 mm^{2}

with a drift velocity of

2 \times 1 0^{- 3} ms^{- 1}

. The number of free electrons in each cubic meter of the wire is:

Answer: (D)

The current carried by free electrons drifting at speed

v_{d}

I = n A e v_{d}

, so

n = \frac{I}{A e v _{d}}

With

A = 5 m m^{2} = 5 \times 1 0^{- 6} m^{2}

n = \frac{10}{( 5 \times 1 0 ^{- 6} ) ( 1.6 \times 1 0 ^{- 19} ) ( 2 \times 1 0 ^{- 3} )} = \frac{10}{1.6 \times 1 0 ^{- 27}} = 6.25 \times 1 0^{27}

The number of free electrons per cubic metre is

625 \times 1 0^{25}

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Single correct option