11.3 Solutions
525
The potential difference between the two spheres is given by
V = −
a
b
E · dr = −
Q
4πε 0
a
b
dr
r 2 =
Q (b − a)
4πε 0 ab
whence C =
Q
V
=
4πε 0 ab
b − a
Fig. 11.45
11.86 By prob. (11.85)
C =
4πε 0 ab
b − a
(1)
Let b = a + where is a small quantity. Then (1) can be written as
C =
4πε 0 a(a + a)
a
4πε 0 a 2
a
(2)
Now the surface area A = 4πa 2 and a = d, the distance between the
surfaces, so that
C
ε 0 A
d
(parallel plate capacitor)
11.87 (i) q = q 0 e −t/RC
e
−t/RC
=
q
q 0
=
90
100
∴
t = RC ln
10
9
= 1 × 10
6
× 10 × 10
−6
× 0.1056 = 1.056 s
525
The potential difference between the two spheres is given by
V = −
a
b
E · dr = −
Q
4πε 0
a
b
dr
r 2 =
Q (b − a)
4πε 0 ab
whence C =
Q
V
=
4πε 0 ab
b − a
Fig. 11.45
11.86 By prob. (11.85)
C =
4πε 0 ab
b − a
(1)
Let b = a + where is a small quantity. Then (1) can be written as
C =
4πε 0 a(a + a)
a
4πε 0 a 2
a
(2)
Now the surface area A = 4πa 2 and a = d, the distance between the
surfaces, so that
C
ε 0 A
d
(parallel plate capacitor)
11.87 (i) q = q 0 e −t/RC
e
−t/RC
=
q
q 0
=
90
100
∴
t = RC ln
10
9
= 1 × 10
6
× 10 × 10
−6
× 0.1056 = 1.056 s