PHY 132 Midterm 2
Mar 31, 2004
Version
Put FULL NAME, ID#, and EXAM VERSION on the front cover of the BLUE BOOKLET!
To avoid problems in grading: do all problems in order
, write legibly
, and show all work for partial credit
!
Note: make sketches where appropriate and show your axis conventions. Do not forget units, number of signifi
cant digits, and check your results for consistency. This exam will last 1.5 hr. Success!
1.
A copper rod of length
D=
0.50 m is pulled with constant velocity
v
= 4.0 m/s, perpendicular to a uniform
and constant magnetic field
B
= 0.25 T, see the Figure. The rod glides without friction on a horizontal U
shaped conductor as shown. Give directions in terms of
up
,
down
,
left
,
right
,
CW
,
CCW
,
into
and
out of
the
paper.
Show all work
!
(60 points)
a.
Calculate the force (magnitude and direction) on an elec
tron (charge –e) in the rod.
Solution:
(10 points)
F
=
q
v
×
B
= –
e vB
(down) = 1.6×10
–19
N (up)
(
B
: 1.6×10
–19
N (down))
a
v
b
D
c
d
B
b.
Calculate the magnitude and direction of the induced emf.
Solution:
(10 points)

E
 =
DvB
= 0.50 V; direction: CW
(
B
: =
LvB
= 0.40 V; CCW)
c.
Assume the resistance of the circuit
abcd
is 0.10
Ω
, constant and dominated by the contact resistance at
points
a
and
b
. Calculate the magnitude of the induced current
I
induced
in the circuit and give its direction.
Solution:
(10 points)
I
= 
E
/R = 5.0 A; direction: CW (
B
: 2.0 A, CCW)
d.
Calculate the magnetic force (magnitude and direction) on the rod due to the induced current.
Solution:
(10 points)
F
M
=
I
D
×
B
=
IDB
(right) = 0.625 N (right) (
B
: =
ILB=
0.160 N (right))
e.
Calculate the power dissipated in the circuit loop.
Solution:
(10 points)
P
=
I
2
R
= 2.5 W (
B
: 0.80 W)
f.
Calculate the magnitude of the external force pulling on the rod.
Solution:
(10 points)
Action is reaction:
F
pull
= –
F
M
= 0.625 (left) (
B
: 0.160 (left))
2.
Consider two long conducting coaxial
cylinders
. The inner cylinder is
solid and has radius
a=
3.0 cm. It carries a uniform current
I
= 900 A in the
direction shown. The outer conducting cylinder has inner radius
b=
10 cm,
and outer radius
c=
11 cm, and carries an
equal
current in the
opposite
di
rection. The space between the cylinders is filled with insulating plastic
(
K
m
= 1.0). Give directions in terms of
up
,
down
,
left
,
right
,
into
and
out of
the the paper.
Show all work!
(30 points)
Q
a
b
c
I
P
a.
Use Ampere’s Law
to calculate the magnetic field for radial distance
i
)
r<a
, and for
ii
)
a<r<b
. Note: for full credit you
must
start from
Ampere’s Law!
Solution:
(14 points)
i
):
2
0
00
22
2
( )
( )
0.200 T/m
2
encl
ra
I
I
dr
B
rI
rB
r
r
r
aa
µ
πµ
π
ππ
<
⋅=
=
=
⇒
=
=
∫
Bl
v