An ionization chamber with parallel conducting plates as

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An ionization chamber with parallel conducting plates as anode and cathode has 5 × 10⁷ electrons and the same number of singly charged positive ions per cm³. The electrons are moving towards the anode with velocity 0.4 m/s. The current density from anode to cathode is 4μA/m². The velocity of positive ions moving towards cathode is

1. 0.4 m/s
2. 1.6 m/s
3. zero
4. 0.1 m/s

Correct Option: D

Current = I_e + I_p
I_e and I_p are current due to electrons and positively charged ions.
I = neAV_d
[ n = 5 × 10⁷ /cm³ = 5 × 10⁷ × 10⁶ / m³ = 5 × 10¹³/m³ ]
I_e = 5 × 10¹³ × 1.6 × 10^-19 × A × 0.4
I_p = 5 × 10¹³ × 1.6 × 10^-19 × A × v
I = I_e + I_p
= 5 × 10¹³ × 1.6 × 10^-19 × A (v + 0.4)
Given,
I/A = 4 × 10^-6 A/m²
4 × 10^-6 A =5 × 10^-6 × 1.6 × A (v + 0.4)

	4	= v + 0.4
	8

⇒ 0.5 = v + 0.4 ⇒ v = 0.1 m/s