Question

if the radius of earth is 6400 kilometer.what is its capacity?

Answer 1

I suppose what is needed is Electrical/electrostatic charge related Capacitance:

  we know that Q = C * V
    Q = charge on the device or material
    C = capacitance
    V = potential difference

For a solid sphere, made of a dielectric material, a charge Q is given to it and then it develops a potential across the substance.   Then the capacity C to hold the electric charge is found by Q/V.

Electro static potential on the surface of sphere of radius R, due to charge resident in it (on the surface or inside) is given by :
       V = 1/(4πε) * Q/R
     => Q / V = 4πε R

    here ε = permittivity of the material of Earth.  It is much more than that of vacuum.    ε = ε₀ K , where K = dielectric constant of the  material of Earth.  K varies from 5 to 30 for soils.  K varies around 80 for Water.

   C = Q/V = 4πε₀ K R
         = 1/(9*10⁹)  K * 6400 * 1000  Farads
         = 0.711 * K    Milli Farads
         = 711 * K    Micro Farads

If K is taken as 15, then the Capacitance is more than 10 milliFarad. 

Usually,  the capacitances  are in the range pico Farads or at most Nano Farads.  So capacitance of 10 milliFarads is very very high.  So Earth can hold a lot of electric charge.  Even water too.  So we use it as the ground or zero potential medium, as a sink for electric discharges.