Aspherical capacitor has an inner sphere of radius 12 cm and an outersphere of radius 13 cm. The outer sphere is earthed and the innersphere is given a charge of 2.5 µC. The space between theconcentric spheres is filled with a liquid of dielectric constant 32.
(a) Determinethe capacitance of the capacitor.
(b) Whatis the potential of the inner sphere?
(c) Comparethe capacitance of this capacitor with that of an isolated sphere ofradius 12 cm. Explain why the latter is much smaller.
Aspherical capacitor has an inner sphere of radius 12 cm and an outersphere of radius 13 cm. The outer sphere is earthed and the innersphere is given a charge of 2.5 µC. The space between theconcentric spheres is filled with a liquid of dielectric constant 32.
(a) Determinethe capacitance of the capacitor.
(b) Whatis the potential of the inner sphere?
(c) Comparethe capacitance of this capacitor with that of an isolated sphere ofradius 12 cm. Explain why the latter is much smaller.
Radius of the innersphere, 
= 12 cm = 0.12 m
Radius of the outersphere, 
=13 cm = 0.13 m
Charge on the innersphere,
Dielectric constant ofa liquid, 
(a) 
Where,
=Permittivity of free space = 
Hence,the capacitance of the capacitor is approximately 
.
(b) Potential ofthe inner sphere is given by,
Hence,the potential of the inner sphere is 
.
(c) Radius of anisolated sphere, r = 12 ×10−2 m
Capacitanceof the sphere is given by the relation,
Thecapacitance of the isolated sphere is less in comparison to theconcentric spheres. This is because the outer sphere of theconcentric spheres is earthed. Hence, the potential difference isless and the capacitance is more than the isolated sphere.
Radius of the innersphere, = 12 cm = 0.12 m
Radius of the outersphere, =13 cm = 0.13 m
Charge on the innersphere,
Dielectric constant ofa liquid,
(a)
Where,
=Permittivity of free space =
Hence,the capacitance of the capacitor is approximately .
(b) Potential ofthe inner sphere is given by,
Hence,the potential of the inner sphere is .
(c) Radius of anisolated sphere, r = 12 ×10−2 m
Capacitanceof the sphere is given by the relation,
Thecapacitance of the isolated sphere is less in comparison to theconcentric spheres. This is because the outer sphere of theconcentric spheres is earthed. Hence, the potential difference isless and the capacitance is more than the isolated sphere.
