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
θ
with the
z
axis as shown in Figure 30-28. Find the magnetic flux through the
coil when (
a
)
θ
= 0
°
, (
b
)
θ
= 30
°
, (
c
)
θ
= 60
°
, and (
d
)
θ
= 90
°
.
(
a
), (
b
), (
c
), (
d
)
φ
m
=
BA
cos
θ
(
a
)
φ
m
= 2
×
10
–1
×
25
×
10
–4
Wb = 5
×
10
–4
Wb = 0.5 mWb;
(
b
)
φ
m
= 0.433 mWb; (
c
)
φ
m
= 0.25 mWb; (
d
)
φ
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. 30-3
(
a
)
φ
m
= [(25
×
7
×
10
–5
×
π
×
25
×
10
–4
) cos 90
°
] Wb = 0
(
b
)
φ
m
= (1.37
×
10
–5
cos 0
°
) Wb = 1.37
×
10
–5
Wb
(
c
)
φ
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. 30-3
(
a
)
φ
m
= (14
×
25
×
10
–4
×
1.2) Wb = 0.042 Wb
(
b
)
φ
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. 30-3
(
a
)
φ
m
= (75
×
π
×
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
φ
m
through the base must also penetrate the spherical surface. Thus,
φ
m
=
π
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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