E
LECTROMAGNETIC
I
NDUCTION
29.7.I
DENTIFY
:
Calculate the flux through the loop and apply Faraday’s law.
S
ET
U
P
:
To find the total flux integrate
B
d
over the width of the loop. The magnetic field of a long straight
wire, at distance
r
from the wire, is
0
2
I
B
r
. The direction of
B
is given by the righthand rule.
E
XECUTE
:
(a)
When
0
2
i
B
r
, into the page.
(b)
0
.
2
B
i
d
BdA
Ldr
r
(c)
0
0
ln( / ).
2
2
b
b
B
B
a
a
iL
dr
iL
d
b a
r
(d)
0
ln(
)
.
2
B
d
L
di
b a
dt
dt
E
(e)
7
0
(0.240 m)
ln(0.360/0.120)(9.60 A/s)
5.06
10
V.
2
E
E
VALUATE
:
The induced emf is proportional to the rate at which the current in the long straight wire is
changing
29.9.I
DENTIFY
and
S
ET
U
P
:
Use Faraday’s law to calculate the emf (magnitude and direction). The direction of the
induced current is the same as the direction of the emf. The flux changes because the area of the loop is
changing; relate
dA
/
dt
to
dc
/
dt
, where
c
is the circumference of the loop.
(a) E
XECUTE
:
2
2
2
and
so
/4
c
r
A
r
A
c
2
( /4 )
B
BA
B
c
2
B
d
B
dc
c
dt
dt
E
At
9.0 s,
1.650 m
(9.0 s)(0.120 m/s)
0.570 m
t
c
(0.500 T)(1/2
)(0.570 m)(0.120 m/s)
5.44 mV
E
(b) S
ET
U
P
:
The loop and magnetic field are sketched in Figure 29.9.
Take into the page to be the
positive direction for
.
A
Then
the magnetic flux is positive.
Figure 29.9
E
XECUTE
:
The positive flux is decreasing in magnitude;
/
B
d
dt
is negative and
E
is positive. By the right
hand rule, for
A
into the page, positive
E
is clockwise.
E
VALUATE
:
Even though the circumference is changing at a constant rate,
/
dA dt
is not constant and
E
is not
constant. Flux
is decreasing so the flux of the induced current is
and this means that
I
is clockwise, which
checks.
29
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
29.16.
I
DENTIFY
:
By Lenz’s law, the induced current flows to oppose the flux change that caus
ed it.
S
ET
U
P
and
E
XECUTE
:
The magnetic field is outward through the round coil and is decreasing, so the magnetic
field due to the induced current must also point outward to oppose this decrease. Therefore the induced current is
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 HKMIET
 Magnetic Field, Lenz

Click to edit the document details