# 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?

Ramesh V
70 Points
14 years ago

(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 Vhig to Vlow

So, the head is at higher potential.

(c)  Vd = drift velocity

Δt  = Δx / Vd

Vd = 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