Electrical Engineering ⇒ Topic : When Inner Sphere is Earthed
When Inner Sphere is Earthed
Figure (a) shows a spherical capacitor when its inner sphere is earthed. Suppose a charge +Q coulomb is given to the outer sphere B. It will now distribute itself over both its inner and outer surfaces. Let out of Q, Q2 coulomb will stay on outer surface of B as it is surrounded by earth all around. The rest charge (Q - Q2), say, Q1 will shift to its inner side because there is earthed sphere A inside B.
The inner charge +Q1 coulomb on inner surface of B induces -Q1 coulomb on A but induced charge +Q1 goes to earth.
Now, it is clear that the two following capacitors are connected in parallel:
(i) One capacitor consists of surface B and the outer surface of A. Its capacitance is given by
(ii) The second capacitor consists of outer surface B and the earth. Its capacitance is given by
C2 = 4πε0r2
Therefore, the total capacitance is given by
When inner sphere is earthed:- Figure A shows the situation.The system constitutes two capacitors in parallel.
(a) One capacitor (CBA) consists of the inner surface of B and outer surface of A. Its capacitance as found above is
(b) The second capacitor (CBG) consists of outer surface of B and earth. Its capacitance is that of an isolated sphere.
... if surrounding medium is air
Total capacitance =CBA+ CBG
NOTE :-Unless stated otherwise, the outer sphere of a sphencal capacitor is assumed to be earthed.
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