A cylindrical conductor of length 2 m and area of cross-section 0.2 mm² carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is α×10⁻³ m²/V s. The value of α is . (Electron concentration =5×10²⁸ /m³ and electron charge =1.6×10⁻¹⁹…

Question

A cylindrical conductor of length 2 m and area of cross-section 0.2 mm² carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is α×10⁻³ m²/V s. The value of α is . (Electron concentration =5×10²⁸ /m³ and electron charge =1.6×10⁻¹⁹ C)

Accepted Answer

1. Field in the wire: E=V/l=2/2=1 V/m. Current density: j=I/A=(1.6)/(0.2×10⁻⁶)=8×10⁶ A/m². Drift speed: v_d=j/(ne)=(8×10⁶)/(5×10²⁸×1.6×10⁻¹⁹)=1×10⁻³ m/s. Mobility μ=(v_d)/E=1×10⁻³ m²/V s, so α=1.

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