If the capacitance of a spherical conductor in air is 2pF
and on keeping it in a medium its capacitance becomes
12 pF, then how much will be the dielectric constant of
the medium?
Answers
Answer:
12th
Physics
Electrostatic Potential and Capacitance
Capacitance and Capacitance
A spherical capacitor consi...
PHYSICS
avatar
Asked on November 22, 2019 by
Suryash Satya
A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig.). Show that the capacitance of a spherical capacitor is given by
c=
r
1
−r
2
4πϵ
0
r
1
r
2
where r
1
and r
2
are the radii of outer and inner spheres, respectively.
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VIDEO EXPLANATION
ANSWER
Radius of the outer shell = r1
Radius of the inner shell = r2
The inner surface of the outer shell has charge +Q.
The outer surface of the inner shell has induced charge −Q.
Potential difference between the two shells is given by,
V=
4πε
o
r
2
Q
−
4πε
o
r
1
Q
Where,
ε
o
= Permittivity of free space
V=
4πε
o
r
2
Q
−
4πε
o
r
1
Q
V=
4πε
o
Q
[
r
2
1
−
r
1
1
]
V=
4πε
o
r
1
r
2
Q(r
1
−r
2
)
Capacitance of the given system is given by,
C=
V
Q
C=
r
1
−r
2
4πε
o
r
1
r
2
Hence, proved.
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