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 v_d(r) = v_0(1−(r/R)). The second wire (wire 2) has the same radius, the same density of charge carriers and a constant drift speed given by v_d(r) = f*v_0. Evaluate the ratio of the current carried by wire 2 to the current carried by wire 1, when f = 0.595.
Note: For the variable drift velocity wire treat the cross-section of the wire as a bunch of differential rings with area = 2πrdr. The differential contribution to the current that passes through a differential ring is given by dI = ?
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