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2663
Chapter 28
Magnetic Induction
Conceptual Problems
1
•
[SSM]
(
a
) The magnetic equator is a line on the surface of
Earth on which Earth’s magnetic field is horizontal.
At the magnetic
equator, how would you orient a flat sheet of paper so as to create the
maximum magnitude of magnetic flux through it? (
b
) How about the
minimum magnitude of magnetic flux?
Determine the Concept
(
a
) Orient the sheet so the normal to the sheet is both horizontal and
perpendicular to the local tangent to the magnetic equator.
(
b
) Orient the sheet of paper so the normal to the sheet is perpendicular to the
direction of the normal described in the answer to Part (
a
).
2
•
At one of Earth’s magnetic poles, how would you orient a flat
sheet of paper so as to create the maximum magnitude of magnetic flux
through it?
Determine the Concept
(
a
) Orient the sheet so the normal to the sheet is vertical.
(
b
) Any orientation as long as the paper’s plane is perpendicular to Earth’s surface
at that location.
3
•
[SSM]
Show that the following combination of SI units is
equivalent to the volt:
T
⋅
m
2
s
.
Determine the Concept
Because a volt is a joule per coulomb, we can show that
the SI units
s
m
T
2
⋅
are equivalent to a volt by making a series of substitutions and
simplifications that reduces these units to a joule per coulomb.
The units of a tesla are
m
A
N
⋅
:
s
A
m
N
s
m
m
A
N
s
m
T
2
2
⋅
=
⋅
⋅
=
⋅
Substitute the units of an ampere
(C/s), replace
m
N
⋅
with J, and
simplify to obtain:
C
J
s
s
C
J
s
m
T
2
=
=
⋅
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2664
Finally, because a joule per coulomb
is a volt:
V
s
m
T
2
=
⋅
4
•
Show that the following combination of SI units is equivalent to the
ohm:
Wb
A
⋅
s
.
Determine the Concept
Because a weber is a newton
⋅
meter per ampere, we can
show that the SI units
Wb
A
⋅
s
are equivalent to an ohm by making a series of
substitutions and simplifications that reduces these units to a volt per ampere.
Because a weber is a
A
m
N
⋅
:
s
A
J
s
A
A
m
N
s
A
Wb
2
⋅
=
⋅
⋅
=
⋅
Substitute the units of an ampere and
simplify to obtain:
C
A
J
s
s
C
A
J
s
A
Wb
⋅
=
⋅
⋅
=
⋅
Finally, because a joule per coulomb
is a volt:
Ω
A
V
s
A
Wb
=
=
⋅
5
•
[SSM]
A current is induced in a conducting loop that lies in a
horizontal plane and the induced current is clockwise when viewed from above.
Which of the following statements could be true? (
a
) A constant magnetic field is
directed vertically downward. (
b
) A constant magnetic field is directed vertically
upward. (
c
) A magnetic field whose magnitude is increasing is directed vertically
downward. (
d
) A magnetic field whose magnitude is decreasing is directed
vertically downward. (
e
) A magnetic field whose magnitude is decreasing is
directed vertically upward.
Determine the Concept
We know that the magnetic flux (in this case the
magnetic field because the area of the conducting loop is constant and its
orientation is fixed) must be changing so the only issues are whether the field is
increasing or decreasing and in which direction. Because the direction of the
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 Summer '08
 Wei

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