CHAPTER
30
Magnetic Induction
1* ·
A uniform magnetic field of magnitude 2000 G is parallel to the
x
axis. A square coil of side 5 cm has a
single turn and makes an angle
?
with the
z
axis as shown in Figure 3028. Find the magnetic flux through the
coil when (
a
)
?
= 0
°
, (
b
)
?
= 30
°
, (
c
)
?
= 60
°
, and (
d
)
?
= 90
°
.
(
a
), (
b
), (
c
), (
d
)
f
m
=
BA
cos
?
(
a
)
f
m
= 2
×
10
–1
×
25
×
10
–4
Wb = 5
×
10
–4
Wb = 0.5
mWb; (
b
)
f
m
= 0.433 mWb; (
c
)
f
m
= 0.25 mWb; (
d
)
f
m
= 0
2
·
A circular coil has 25 turns and a radius of 5 cm. It is at the equator, where the earth's magnetic field is 0.7
G north. Find the magnetic flux through the coil when its plane is (
a
) horizontal, (
b
) vertical with its axis pointing
north, (
c
) vertical with its axis pointing east, and (
d
) vertical with its axis making an angle of 30
°
with north.
(
a
), (
b
), (
c
) Use Equ. 303
(
a
)
f
m
= [(25
×
7
×
10
–5
×
p
×
25
×
10
–4
) cos 90
°
] Wb = 0
(
b
)
f
m
= (1.37
×
10
–5
cos 0
°
) Wb = 1.37
×
10
–5
Wb
(
c
)
f
m
= (1.37
×
10
–5
cos 30
°
) Wb = 1.19
×
10
–5
Wb
3
·
A magnetic field of 1.2 T is perpendicular to a square coil of 14 turns. The length of each side of the coil is
5 cm. (
a
) Find the magnetic flux through the coil. (
b
) Find the magnetic flux through the coil if the magnetic field
makes an angle of 60
°
with the normal to the plane of the coil.
(
a
), (
b
) Use Equ. 303
(
a
)
f
m
= (14
×
25
×
10
–4
×
1.2) Wb = 0.042 Wb
(
b
)
f
m
= (0.042 cos 60
°
) Wb = 0.021 Wb
4
·
A circular coil of radius 3.0 cm has its plane perpendicular to a magnetic field of 400 G. (
a
) What is the
magnetic flux through the coil if the coil has 75 turns? (
b
) How many turns must the coil have for the flux to be
0.015 Wb?
(
a
), (
b
) Use Equ. 303
(
a
)
f
m
= (75
×
p
×
9
×
10
–4
×
4
×
10
–2
) Wb = 8.48 mWb
(
b
)
N
= 75(15/8.48) = 133
5* ·
A uniform magnetic field
B
is perpendicular to the base of a hemisphere of radius
R
. Calculate the magnetic
flux through the spherical surface of the hemisphere.
Note that
f
m
through the base must also penetrate the spherical surface. Thus,
f
m
=
p
R
2
B
.
6
··
Find the magnetic flux through a solenoid of length 25 cm, radius 1 cm, and 400 turns that carries a current
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View Full DocumentChapter 30
Magnetic Induction
of 3 A.
Use Equs. 299 and 303;
f
m
=
μ
0
N
2
AI
/
L
f
m
= 7.58
×
10
–4
Wb
7
··
Work Problem 6 for an 800turn solenoid of length 30 cm, and radius 2 cm, carrying a current of 2 A.
Use Equs. 299 and 303;
f
m
=
μ
0
N
2
AI
/
L
f
m
= 6.74
×
10
–3
Wb
8
··
A circular coil of 15 turns of radius 4 cm is in a uniform magnetic field of 4000 G in the positive
x
direction.
Find the flux through the coil when the unit vector perpendicular to the plane of the coil is (
a
)
n
=
i
, (
b
)
n
=
j
, (
c
)
n
= (
i
+
j
)/
2
, (
d
)
n
=
k
, and (
e
)
n
= 0.6
i
+ 0.8
j
.
(
a
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 Spring '08
 MILLAN/THORSTENSEN
 Physics, Flux, Magnetic Field

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