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:

                                                           figure (a)

(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 (C_BA) consists of the inner surface of B and outer surface of A. Its capacitance as found above is

                                                                                     FIGURE (A)

 (b) The second capacitor (C_BG) consists of outer surface of B and earth. Its capacitance is that of an isolated sphere.

                   ... if surrounding medium is air

                  Total capacitance =C_BA+ C_BG

NOTE :-Unless stated otherwise, the outer sphere of a sphencal capacitor is assumed to be earthed.