This preview shows pages 1–3. Sign up to view the full content.
Chapter 28
Magnetic Induction
20
•
A uniform magnetic field of magnitude 0.200 T is in the +
x
direction. A square coil that has 5.00cm
long sides has a single turn and makes an angle
θ
with the z axis, as shown in Figure 2842.
Find the magnetic
flux through the coil when
is (
a
) 0º, (
b
) 30º, (
c
) 60º, and (
d
) 90º.
Picture the Problem
Because the surface is a plane with area
A
and
B
is constant
in magnitude and direction over the surface and makes an angle
with the unit
normal vector, we can use
φ
cos
m
BA
=
to find the magnetic flux through the
coil.
The magnetic flux through the coil is
given by:
cos
m
BA
=
Substitute for
B
and
A
to obtain:
(
29
(
29
cos
Wb
10
00
.
5
cos
m
10
5.00
G
10
T
1
G
2000
4
2
2
4
m


×
=
×
⋅
=
(
a
) For
= 0
°
:
(
29
mWb
50
.
0
Wb
10
00
.
5
0
cos
Wb
10
00
.
5
4
4
m
=
×
=
°
×
=


(
b
) For
= 30
°
:
(
29
mWb
43
.
0
Wb
10
33
.
4
cos30
Wb
10
00
.
5
4
4
m
=
×
=
°
×
=


(
c
) For
= 60
°
:
(
29
mWb
25
.
0
Wb
10
50
.
2
cos60
Wb
10
00
.
5
4
4
m
=
×
=
°
×
=


(
d
) For
= 90
°
:
(
29
0
cos90
Wb
10
00
.
5
4
m
=
°
×
=

6
•
Give the direction of the induced current in the circuit, shown on the right in Figure 28 37, when the
resistance in the circuit on the left is suddenly
(
a
) increased and (
b
) decreased. Explain your answer.
Determine the Concept
The induced emf and induced current in the circuit on
the right are in such a direction as to oppose the change that produces them
(Lenz’s Law). We can determine the direction of the induced current in the
circuit. Note that when
R
is constant,
B
in the circuit to the right points out of the
paper.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document(
a
) If
R
increases,
I
decreases and
B
in the circuit to the right decreases. Lenz’s
law tells us that the induced current is counterclockwise.
(
b
) If
R
decreases,
I
increases and
B
in the circuit to the right increases. Lenz’s
law tells us that the induced current is clockwise.
32
•
A solenoid that has a length equal to 25.0 cm, a radius equal to
0.800 cm, and 400 turns is in a region where a magnetic field of 600 G exists and makes an angle of 50º with
the axis of the solenoid. (
a
) Find the magnetic flux through the solenoid. (
b
) Find the magnitude of the average
emf induced in the solenoid if the magnetic field is reduced to zero in 1.40 s.
Picture the Problem
We can use its definition to find the magnetic flux through
the solenoid and Faraday’s law to find the emf induced in the solenoid when the
external field is reduced to zero in 1.4 s.
(
a
) Express the magnetic flux
through the solenoid in terms of
N
,
B
,
A
,
and
θ
:
π
φ
cos
cos
2
m
R
NB
NBA
=
=
Substitute numerical values and
evaluate
m
:
(
29 (
29
(
29
mWb
1
.
3
mWb
10
.
3
50
cos
m
00800
.
0
mT
0
.
60
400
2
m
=
=
°
=
(
b
) Apply Faraday’s law to obtain:
mV
2
.
2
s
1.40
mWb
3.10
0
m
=


=
∆
∆

=
t
ε
36
••
A 30.0cm long rod moves steadily at 8.00 m/s in a plane that is perpendicular to a magnetic field of
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Turner
 Physics

Click to edit the document details