The diagram shows two wires; wire 1 and wire 2. The charge carriers in wire 1 (o

Question

The diagram shows two wires; wire 1 and wire 2. The charge carriers in wire 1 (of circular cross section and radius R) have a drift speed down the wire that is not constant across the wire. Instead, the drift speed rises from zero at the circumference (r=R) to v0 at the center (r = 0), according to vd(r) = v0(1(rR)) . The second wire (wire 2) has the same radius, the same density of charge carriers and a constant drift speed given by vd(r) = fv0. Evaluate the ratio of the current carried by wire 2 to the current carried by wire 1, when f = 0.560.

Explanation / Answer

given

two wires with currents i1,i2

given drift speed is  

Vd = J/ne

Vd = i/(n*e*A)

n is current density and A is area of cross section of the wire

for wire 1 , vd1(r) = V0(1-(rR))

for wire 2 , vd2(r) = fV0 , f = 0.560

vd = i/(n*e*A)

i = vd*n*e*A

now i2/i1 = (vd2*n*e*A2)/(vd1*n*e*A1)

i2/i1 = (vd2)/(vd1)

i2/i1 = (0.560*V0)/(V0(1-(rR))

i2/i1 = 0.560 /(1-r*R)

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