The Total solution for NCERT class 6-12
A spherical capacitor has an inner sphere of radius 12 cmand an outer sphere of radius 13 cm. The outer sphere is earthed and the innersphere is given a charge of 2.5 µC. The space between the concentric spheres isfilled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with thatof an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
Radius of the innersphere, = 12 cm = 0.12 mRadius of the outer sphere, = 13 cm = 0.13 mCharge on the inner sphere,
Where,
= Permittivity of freespace =
Hence, the capacitance ofthe capacitor is approximately
(b) Potential of the inner sphere is given by,
Hence, the potential of theinner sphere is
(c) Radius of an isolated sphere, r = 12 ×10−2 m
Capacitance of the sphere is given by the relation,
The capacitance of the isolated sphere isless in comparison to the concentric spheres. This is because the outer sphereof the concentric spheres is earthed. Hence, the potential difference is lessand the capacitance is more than the isolated sphere.