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PHYSICS 222, FALL 2005
EXAM #1 SOLUTIONS
SEPTEMBER 29, 2005
Note:
i
ˆ
,
j
ˆ
, and
k
ˆ
are unit vectors directed in the +x, +y, and +z directions, respectively, of a righthanded
Cartesian coordinate system.
Problems 115 are worth 2 points each.
1.
At some instant of time, a negatively charged particle is moving with velocity
v
→
= v
i
ˆ
in a magnetic field
B
→
= B
k
ˆ
, where v is the particle's speed and B is the magnitude of
B
→
.
The direction of the magnetic
force on the particle is ____ .
A.
i
ˆ
B.
−
i
ˆ
C.
−
j
ˆ
D.
j
ˆ
E.
k
ˆ
Since the particle has a negative charge q, one has q =
−
q.
Thus,
F
→
=
q
v
→
×
B
→
=
−
qvB (
i
ˆ
×
k
ˆ
)
=
−
qvB (
−
j
ˆ
)
=
qvB
j
ˆ
.
2.
A currentcarrying circular coil with a magnetic moment
µ
→
is in a uniform magnetic field
B
→
.
The
maximum magnitude of the magnetic torque on the coil occurs when the angle between
µ
→
and
B
→
is ____
degrees.
A.
0
B.
45
C.
90
D.
135
E.
180
τ
=
µ
B sin
φ
, so the maximum torque occurs when
sin
φ
=
1, giving
φ
=
90˚ .
3.
A sphere of radius R is in a uniform magnetic field of magnitude B.
The magnitude of the net magnetic
flux through the surface of the sphere is ____ .
A.
0
B.
π
R
2
B
C.
2
π
R
2
B
D.
4
π
R
2
B
E.
8
π
R
2
B
For a closed surface, Gauss' law for magnetism is
Φ
B
=
∫
O
B
→
· d
A
→
=
0 .
4.
Two long thin straight parallel wires each carry the same magnitude of current I but in opposite
directions.
The distance between the axes of the wires is d.
The magnitude of the (net) magnetic field at
a point midway between the two axes of the wires is ____.
Using the circular righthand rule, one finds that each wire produces a magnetic field at P that is in the
same direction.
Since the distance from P to the axis of each wire (= d/2) is the same, the magnitude of
the field contribution from each wire is the same:
B
=
µ
o
I/(
π
d).
The sum of these two magnitudes is
twice the value for each one:
B
=
2
µ
o
I/(
π
d) .
5.
The magnetic field at the center of a circular wire loop of radius R and carrying a current I ____
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 Fall '05
 Ogilvie
 Physics, Magnetic Field, Faraday, A., a. b. c., b. c. d., A. B. C. D.

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