Chapt. 27 Currents and Resistance 205
5.
for a single kind of charge carrier of charge
q
is deFned by
v
J
=
nqvV ,
where
n
is the density of charge carriers at that point and
vV
is the velocity of the charge carriers
at some point.
is a vector and note that it points opposite to
vV
when
q <
0.
Imagine a horizontal di±erential bit of surface area
dA
. The net charge ²owing through this
area in a direction an angle
θ
from the vertical in time Δ
t
is
Δ
Q
=
nq
(
V
Δ
t
)
dA
cos
θ
= (
nqvV
·
d
v
A
)Δ
t
= (
v
J
·
d
v
A
)Δ
t ,
where (
V
Δ
t
)
dA
cos
θ
is the volume of a parallelepiped that sweeps through
dA
in Δ
t
,
V
Δ
t
is
the length of one side of the parallelepiped, and
d
v
A
is the vectorized di±erential area. The
di±erential current through
d
v
A
is
dI
=
v
J
·
d
v
A .
Integrating over a Fnite surface gives a current:
I
=
i
surface
v
J
·
d
v
A .
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 Fall '06
 Buchler
 Physics, Electron, Charge, Current, Resistance, Electric charge, Fundamental physics concepts

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