A copper wire of radius 1 mm contains 10²² free electrons per cubic metre. The drift velocity for free electrons when 10 A current flows through the wire will be (Given, charge on electron = 1.6 × 10⁻¹⁹ C): (a) 6.25 × 10⁴π m s⁻¹ (b) (6.25)/(π) × 10³ m s⁻¹ (c) (6.25)/(π) m s⁻¹ (d) 6.25 × 10⁵π m s⁻¹

Answer: (b). I = neAvd ⇒ vd = I/neA, with A = π r² = π × 10⁻⁶ m² vd = 1010²² × 1.6 × 10⁻¹⁹ × π × 10⁻⁶ = 101.6 × 10⁻³ π vd = 6.25 × 10³π m s⁻¹ So the answer is (b).

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Q8NEET 2023Easy

Electric Current, Drift Velocity & Current Density

A copper wire of radius $1\text{ mm}$ contains $10^{22}$ free electrons per cubic metre. The drift velocity for free electrons when $10\text{ A}$ current flows through the wire will be (Given, charge on electron $= 1.6 \times 10^{-19}\text{ C}$ ):

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Answer: (b)

$I = neAv_d \Rightarrow v_d = \dfrac{I}{neA}$ , with $A = \pi r^{2} = \pi \times 10^{-6}\text{ m}^{2}$
$v_d = \dfrac{10}{10^{22} \times 1.6 \times 10^{-19} \times \pi \times 10^{-6}} = \dfrac{10}{1.6 \times 10^{-3}\,\pi}$
$v_d = \dfrac{6.25 \times 10^{3}}{\pi}\text{ m s}^{-1}$
So the answer is (b).

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