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NCERT Class XII Chapter
Electrostatic Potential and Capacitance
Questions With Solutions

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Question : 29
Total: 37
A spherical capacitor consists of two concentric spherical conductors held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by C =
4πε0r1r2
r1−r2
Where r1 and r2 are the radii of outer and inner spheres, respectively.
Solution:  

Let + Q be the charge on outer spherical shell A of radius r1 and + Q be the charge on inner spherical shell B of radius r2. Then electric potential on shell A is
VA = VAA+VAB =
1
4πε0
 [+
Q
r1
−
Q
r1
] or VA = 0
and electric potential on shell B is
VB = VBA+VBB =
1
4πε0
[
Q
r1
−
Q
r2
]
or VB =
Q
4πε0
 [
r2−r1
r1r2
]
So, the potential difference between the two spherical shells A and B is
V = VA−VB = 0 -
Q
4πε0
[
r2−r1
r1r2
]
or V =
Q
4πε0
[
r2−r1
r1r2
] or
Q
V
 =
4πε0r1r2
r1r2
 or
Q
V
 =
4πε0r1r2
r1−r2
 or C =
4πε0r1r2
r1−r2
This gives the capacitance of the spherical capacitor.
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