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 1 
Physics 2213 HW #14 — Solutions
Fall 2008
30.6
[Inductor]
A changing current in an inductor induces an emf in it.
(a)
The selfinductance of a toroidal solenoid is
2
0
.
2
N A
L
r
μ
π
=
7
2
4
2
4
(4
10
T m/A)(500) (6.25 10 m )
7.81 10 H
2 (0.0400 m)
L



×
⋅
×
=
=
×
This is a reasonable value for selfinductance, in the range of a mH.
(b)
The magnitude of the induced emf is
.
di
L
dt
=
E
( 29
4
3
5.00 A
2.00 A
7.81 10 H
0.781 V
3.00 10 s



=
×
=
×
E
(c)
The current is decreasing, so the induced emf will be in the same direction as the current, which is
from
a
to
b,
making
b
at a higher potential than
a.
30.19
[LR Circuit]
Apply Kirchhoff’s loop rule to the circuit.
i
(
t
) is given by Eq.(30.14).
di
dt
is positive as the current
increases from its initial value of zero.
0
R
L
v
v


=
E
( 29
( / )
0 so
1
R L t
di
iR
L
i
e
dt
R



=
=

E
E
(a)
Initially (
t
= 0),
i
= 0 so
0
di
L
dt

=
E
6.00 V
2.40 A/s
2.50 H
di
dt
L
=
=
=
E
(b)
0
di
iR
L
dt


=
E
(Use this equation rather than Eq.(30.15) since
i
rather than
t
is given.)
Thus
6.00 V
(0.500 A)(8.00
)
0.800 A/s
2.50 H
di
iR
dt
L


Ω
=
=
=
E
(c)
( 29
( 29
( / )
(8.00 /2.50 H)(0.250 s)
0.800
6.00 V
1
1
0.750 A(1
)
0.413 A
8.00
R L t
i
e
e
e
R


Ω

=

=

=

=
Ω
E
(d)
Final steady state means
and
0, so
0.
di
t
iR
dt
→ ∞
→

=
E
6.00 V
0.750 A
8.00
i
R
=
=
=
Ω
E
Our results agree with Fig.30.12 in the textbook. The current is initially zero and increases to its final
value of
/ .
R
E
The slope of the current in the figure, which is
di/dt
, decreases with
t
.
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30.43
[Mutual Inductance]
The emf
2
E
in solenoid 2 produced by changing current
1
i
in solenoid 1 is given by
1
2
.
i
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This note was uploaded on 08/27/2009 for the course PHYS 2213 taught by Professor Perelstein,m during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 PERELSTEIN,M
 Current, Inductance, Magnetism, Heat

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