210Chapt. 27Currents and Resistancea) In which direction does each kind of ion move?b) Given that the conductivity of the air is given byσ= 2.70×10−14Ω−1m−1, what is thecurrent density?c) Assume that the ions have the same drift speed which is plausible since they are in the sameelectric field, have about the same mass on average, the same absolute value of charge, andabout the same collision time on average. Recall in thatvectorJ=nqvectorvd,wherenis carrier density,qis carrier charge, andvectorvdis the drift velocity.What is this drift speed in our case? (Note that current is net flux of charge, not fluxof one kind or another of charge. Be careful about signs.)027 qfull 00300 1 3 0 tough math: deriving Ohm’s law5. We will now derive Ohm’s law in its usual form (which is what one means when one just saysOhm’s law without qualification) from the microscopic form of Ohm’s law.The microscopicform of Ohm’s law isvectorJ=σvectorEwherevectorJ
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