Physics 213
Homework 10 Solutions
Spring 2009
Q30.2
[Transformer]
Transformers work because of Faraday's Law of magnetic induction — a changing magnetic flux
produces an induced emf.
Since the areas and orientations of the transformer's coils are fixed, a changing magnetic field
is required to produce a changing magnetic flux, which requires a changing electric current.
The induced emf
2
= N
2
(d
B
/dt) in the secondary coil is nonzero as long as the electric current i
1
in the primary coil is changing.
A DC (constant) current won't produce a changing magnetic flux, so a transformer won't work with DC.
An
AC current is needed since it is always changing.
30.9
[Inductor]
(a)
3
(0.260 H)(0.0180 A/s) 4.68 10 V
L di dt
(b)
From Figure 30.6 on page 1036 of the textbook, we see that the rule is
V
cd
=Ldi/dt
, where
c
is the upstream point and
d
is the downstream point as defined by the current.
In our case, the current goes from
b
to
a
, so
V
ba
=Ldi/dt<0
.
This
means
V
b
V
a
<0
, so
V
a
>V
b
.
The inductor acts like a battery with its + terminal facing
a
to fight the change in current.
30.10.
[Inductor]
In this problem, we apply
L
di
dt
.
Since
i
is changing at a constant rate,
di
i
t
dt
.
(a)
The induced emf points from low potential to high potential across the inductor.
In this case, the induced emf points
from
b
to
a
, in the direction of the current. Therefore, the current is decreasing and the induced emf is directed to oppose
this decrease.
(b)
L
i
/
t
,so
i
/
t
V
ab
/
L
(1.04 V) / (0.260 H)
4.00 A/s. In 2.00 s the decrease in
i
is 8.00 A and the
current at 2.00 s is
12.0 A
8.0 A
4.0 A.
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 Spring '07
 PERELSTEIN,M
 Magnetism, Work, Heat, Magnetic Field, Inductor, Energy density, Faraday's law of induction, magnetic energy

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