PHY2049 Fall 2007
1
Prof. Yasu Takano
Prof. Paul Avery
Oct. 17, 2007
Exam 2 Solutions
1. (
WebAssign 26.6
) A current of 1.5 A flows in a copper wire with radius 1.25 mm. If the cur-
rent is uniform, what is the electron drift speed in m/s? Copper has a density of 8960 kg/m
3
,
atomic mass of 63.54 and one conduction electron per atom.
(1) 2.2
×
10
−
5
(2) 3.6
×
10
−
4
(3) 5.4
×
10
−
3
(4) 7.4
×
10
−
4
(5) 3.0
×
10
−
5
The current density j is given by
2
/
e d
j
i
r
en v
π
=
=
, where n
e
is the conduction electron density
and v
d
is the drift velocity. The electron number density for copper is the same as the atomic den-
sity since there is one conduction electron per atom. That calculation gives the electron number
density
(
)
3
23
28
0
/10
8960
6.02
10
/ 0.06354
8.49
10
e
Cu
n
N
A
ρ
−
=
=
×
×
=
×
/m
3
, where the factor of
10
−
3
is the conversion from g to kg in the atomic mass. Using
2
/
j
i
r
π
=
, we obtain v
d
= 2.2
×
10
−
5
m/s.
2. (
WebAssign 26.41
) A heating element is made by maintaining a potential difference of 60.0 V
along the length of a Nichrome wire with radius 0.945 mm and a resistivity of 5.00
×
10
−
7
Ω
m.
If the element dissipates 5000 W, what is its length in m?
(1) 4.0
(2) 5.2
(3) 2.2
(4) 0.56
(5) 0.22
The power dissipated is
2
2
/
P
i R
V
R
=
=
, where
/
R
L
A
ρ
=
,
ρ
is the resistivity, L is the length
and A =
π
r
2
is the cross sectional area. Putting in all the numbers yields L = 4.0 m.

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