PHY2049 Spring 2010
Profs. P. Avery, A. Rinzler, S. Hershfield
Exam 3 Solution
1. An AC power supply drives a 270 mH inductor. The power supply EMF is
E
=
E
m
sin
ω
d
t
, where
E
m
= 12
V
and
ω
d
= 120
rad/s. When the instantaneous current in the circuit is a maximum, the instantaneous emf of the power supply is
Answer:
0 V
Solution:
The current through and voltage across an inductor are 90
◦
out of phase.
Thus, when the current is a
maximum, the voltage is zero.
2. Oxygen:
(A) has an intrinsic magnetic dipole moment,
(B) is paramagnetic,
(C) is attracted to the high field point of a nonuniform magnetic field,
(D) is diamagnetic.
Of these statements
only
the following are true,
Answer:
A, B & C
Solution:
As shown in the demonstration performed in class, oxygen is attracted to the high field point because it has
an intrinsic dipole moment and is paramagnetic.
3. In the figure the instantaneous current charging the capacitor is
i
= 1
.
2 A.
The circular capacitor plates have a radius of 20 cm. The magnitude of the
magnetic field at the point labeled p that lies between the plates, 15 cm from
the centerline between the plates is
Answer:
9
.
0
×
10
−
7
T
Solution:
For this problem use
contintegraltext
vector
B
·
dvectors
= 2
πrB
=
μ
o
i
d
, where
i
d
is the displacement current through a circle of radius
r
= 0
.
15
m
. This is not the total displacement current between the disks, 1
.
2 A, because the circle of radius
r
= 0
.
15
m
does not enclose all of the electric flux. It encloses a fraction of the electric flux: (
π
0
.
15
2
)
/
(
π
0
.
2
2
) = (0
.
75)
2
. Solve for
B
using 2
π
(0
.
15
m
)
B
=
μ
o
(0
.
75)
2
(1
.
2
A
).
4. The magnetic flux
entering
the circular bottom face of a right circular cylinder is 23
.
4 T
·
m
2
and the magnetic flux
exiting
the sidewall of the cylinder is 63
.
9 T
·
m
2
. The magnetic flux on the top face must be
Answer:
40
.
5 T
·
m
2
, entering
Solution:
The net magnetic flux through the cylinder must be zero. The flux from two of the surfaces is 63
.
9
−
23
.
4 =
40
.
5 T
·
m
2
exiting the cylinder. Thus, the remaining surface must have 40
.
5 T
·
m
2
entering the cylinder.
5. The circular region of radius
r
= 50 cm shown in the figure contains a uniform electric
field pointing into the page that is increasing according to
E
(
t
) = 2
.
4
×
10
5
t
(in units
of V/m), where
t
is in seconds. For the path indicated by the dotted line what is the
magnitude of
contintegraltext
vector
B
·
dvectors
, in units of T
·
m?
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 Spring '08
 Any
 Physics, Current, Inductance, Power, Inductor, LC circuit

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