Electrical Engineering ⇒ Topic : When Outer Sphere is Earthed

When Outer Sphere is Earthed

Figure (a) shows a spherical capacitor. Let the radius of its inner and outer sphere be r₁ and r₂ metre, respectively. Suppose, the inner sphere is given a charge of +Q coulomb. Therefore, it will induce Q coulomb on inner surface of outer sphere and a charge +Q coulomb on the outer surface of the outer sphere will go to earth. Let the relative permittivity of the dielectric medium between the two spheres be Er. The surface potential of the inner sphere due to +0 coulomb is given by

                                              figure (a)   Outer sphere earthed

The surface potential of inner surface of outer sphere due to -Q coulomb is given by

Therefore, the total potential difference between the two surfaces is given by

Therefore, the capacitance of the sphere is given by

                                                                                                .............. (1)

When outer sphere is earthed. A spherical capacitor consists of two concentric hollow metallic spheres A and B which do not touch each other as shown in Figure(a). The outer sphere B is earthed while charge is given to the inner sphere A. Suppose the medium between the two sphere has relative permittivity εr

                                                  FIGURE (A)

When a charge +Q is given to the inner sphere A, it induce a charge -Q on the inner surface of outer sphere B and +Q on thc outer surface of B. Since sphere B is earthed, +Q charge on outer surface is neutralised by earth.

*Potential at inner sphere A,V_A =

Since sphere B is earthed, its potential is zero (i.e., V_B = 0)

P.D. between A and B, V_AB  =  V_A  -  V_B  = V_A -  0 = V_A

Capacitance of spherical capacitor, C =

                                                       ... ....   in   a  medimum

                                                                  .....    in air

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