210
Chapt. 27
Currents and Resistance
a) In which direction does each kind of ion move?
b) Given that the conductivity of the air is given by
σ
= 2
.
70
×
10
−
14
Ω
−
1
m
−
1
, what is the
current density?
c) Assume that the ions have the same drift speed which is plausible since they are in the same
electric field, have about the same mass on average, the same absolute value of charge, and
about the same collision time on average. Recall in that
vector
J
=
nqvectorv
d
,
where
n
is carrier density,
q
is carrier charge, and
vectorv
d
is the drift velocity.
What is this drift speed in our case? (Note that current is net flux of charge, not flux
of one kind or another of charge. Be careful about signs.)
027 qfull 00300 1 3 0 tough math: deriving Ohm’s law
5. We will now derive Ohm’s law in its usual form (which is what one means when one just says
Ohm’s law without qualification) from the microscopic form of Ohm’s law.
The microscopic
form of Ohm’s law is
vector
J
=
σ
vector
E
where
vector
J
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 Fall '06
 Buchler
 Physics, Conductivity, Current, Resistance, conductor

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