82
Capacitance and Dielectrics
P26.10
With
θπ
=
, the plates are out of mesh and the overlap area is zero. With
θ
=
0 , the overlap area is that of a semicircle,
π
R
2
2
. By proportion, the
effective area of a single sheet of charge is
πθ
−
af
R
2
2
When there are two plates in each comb, the number of adjoining
sheets of positive and negative charge is 3, as shown in the sketch. When
there are
N
plates on each comb, the number of parallel capacitors is
21
N
−
and the total capacitance is
FIG. P26.10
CN
A
NR
d
d
=−
∈
=
−∈ −
=
2
2
0
0
2
0
2
a
f
a
f
a
f
a
f
a
f
effective
distance
.
P26.11
(a)
C
k
e
b
a
==
×
=
A
2
50 0
2 8 99 10
268
9
727
258
ln
.
.l
n
.
.
.
ch
ej
nF
(b)
Method 1:
∆
Vk
b
a
e
=
F
H
G
I
K
J
2
λ
ln
×
=×
×
F
H
G
I
K
J
=
−
−
−
q
V
A
810 10
162 10
2 8 99 10
1 62 10
302
6
7
97
.
.
..
l
n
.
.
.
C
50.0 m
Cm
kV
∆
e
j
Method 2:
∆
V
Q
C
×
×
=
−
−
268 10
6
9
.
.
.
k
V
P26.12
Let the radii be
b
and
a
with
ba
=
2 . Put charge
Q
on the inner conductor and
–Q
on the outer.
Electric field exists only in the volume between them. The potential of the inner sphere is
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Capacitance, Charge

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