http://capa.mcgill.ca/res/mcgill/dcmcgill/bytopic/23a-currents-ohms-law/figs/23a

Question

http://capa.mcgill.ca/res/mcgill/dcmcgill/bytopic/23a-currents-ohms-law/figs/23a-0013.gif The diagram above 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 linearly from zero at the circumference (r = R) to v0 at the center (r = 0), according to vd(r) = v0(1-r/R). A second wire (wire 2) has the same radius, the same density of charge carriers and a constant drift speed given by vd(r) = f*v0. Evaluate the ratio of the current carried by wire 1 to the current carried by wire 2, when f = 0.525. My prof said I need to integrate to get the current of the first wire dI=nqv(r)2pi rdr but I don't really understand how or why. Can someone please explain?

Explanation / Answer

Since the drift speed varies along the radius, so integration needs to be done as you have to take contribution of each annular ring of thickness dr located at r from center, in order to get the total current.

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