Ques1) A caterpiller of length 4cm crawls in the direction of electron drift along a 5.2mm diameter bare copper wire that carries an uniform current of 12 A. (a) What is the potential difference b/w the two ends of the caterpiller? (b) Is it's tail positive or negative relative to the head? (c) How much time does it takes to crawl 1 cm if it crawlsat the drift speed of the electrons in the wire? (The number of vharge carries per unit volume is 8.49 x 10 ²⁸ m^-3.)

Ques2) What would happen to the drift velocity of the electrons in a wire and to the current in the wire if the electrons could move freely without the resistance through the wire?

(1)

Area of copper wire : Pi/d*d² = 2.123x10^-5 m² 

lenght of catrepillar : L : 0.04 m

Resistivity of copper is: 1.69 x 10^-8 ohm-meter

no. density of charge carriers in copper: ρ = 8.49 x 10 ²⁸ m^-3

 (a) volatge V = iR = iρL/A

                 V = (12*1.69 * 10^-8 * 4*10^-2) / 2.123x10^-5

                    = 0.382 mV

  (b) current i is opposite to electron drift

        i runs from V_hig to V_low

        So, the head is at higher potential.

 (c)  V_d = drift velocity

        Δt  = Δx / V_d

        V_d = J / ne = i / Ane

       Δt  = Δx .Ane /i

             = 10-2 * 2.123x10^-5 *8.49*10²⁸ *1.602*10^-19 / 12

             =  240.5 sec

time it takes to crawl is 240.5 sec

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IIT Kgp - 2005 batch