PHYS 241
Ch. 24 Homework Solutions
24.5.I
DENTIFY
:
ab
Q
C
V
=
.
0
A
C
d
=
P
.
S
ET
U
P
:
When the capacitor is connected to the battery,
12.0 V
ab
V
=
.
E
XECUTE
:
(a)
6
4
(10.0 10 F)(12.0 V) 1.20 10 C 120
C
ab
Q
CV
μ


= = × = × =
(b)
When
d
is doubled
C
is halved, so
Q
is halved.
60
C
Q
=
.
(c)
If
r
is doubled,
A
increases by a factor of 4.
C
increases by a factor of 4 and
Q
increases by a factor
of 4.
480
C.
Q
=
E
VALUATE
:
When the plates are moved apart, less charge on the plates is required to produce the same
potential difference. With the separation of the plates constant, the electric field must remain constant
to produce the same potential difference. The electric field depends on the surface charge density,
σ
.
To produce the same
, more charge is required when the area increases.
24.11.
I
DENTIFY
and
S
ET
U
P
:
Use the expression for
C
/
L
derived in Example 24.4. Then use Eq.(24.1) to
calculate
Q.
E
XECUTE
:
(a)
From Example 24.4,
(
29
0
2
ln
/
b
a
C
L
r r
π
=
P
(
29
(
29
12
2
2
11
2
8.854 10
C / N m
6.57 10
F/m
66 pF/m
ln 3.5 mm/1.5 mm
C
L


×
⋅
=
=
×
=
(b)
(
29
(
29
11
10
6.57 10
F/m 2.8 m
1.84 10
F.
C


=
×
=
×
(
29
(
29
10
3
11
1.84 10
F 350 10 V
6.4 10
C
64 pC
Q
CV



=
=
×
×
=
×
=
The conductor at higher potential has the positive charge, so there is +64 pC on the inner conductor and
64

pC on the outer conductor.
E
VALUATE
:
C
depends only on the dimensions of the capacitor.
Q
and
V
are proportional.
24.15.
I
DENTIFY
:
Replace series and parallel combinations of capacitors by their equivalents. In each
equivalent network apply the rules for
Q
and
V
for capacitors in series and parallel; start with the
simplest network and work back to the original circuit.
S
ET
U
P
:
Do parts
(a)
and
(b)
together. The capacitor network is drawn in Figure 24.15a.
1
2
3
4
400
F
C
C
C
C
=
=
=
=
28.0 V
ab
V
=
Figure 24.15a
E
XECUTE
:
Simplify the circuit by replacing the capacitor combinations by their equivalents:
1
2
and
C
C
are in series and are equivalent to
12
C
(Figure 24.15b).
12
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 Fall '08
 Milsom
 Magnetism, Energy, Work, Electric charge

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