2.30 A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 \muC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.

(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.

Answers (1)

The radius of the isolated sphere r = 4.5*10^2

Now, Capacitance of sphere:

C_{new}=4\pi\epsilon _0r=4\pi 8.85*10^{-12}*12*10^{-12}=1.33*10^{-11}F

ON comparing it with the concentric sphere, it is evident that it has lesser capacitance.this is due to the fact that the concentric sphere is connected to the earth.

Hence the potential difference is less and capacitance is more than the isolated sphere.  

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