Question

when the radius of earth is 6400 km,the capacitance of earth is:

Answer 1

When a solid sphere or a hollow sphere of radius R  is given a charge Q, the charge is equally distributed all around the surface of sphere.  The electric potential is same all around the surface of sphere.  

The electric field on the surface of Sphere E = 1/(4πε) * Q / R²
The electric potential on the surface of sphere = V = 1/(4πε) * Q / R

Capacitance of a substance or device = C = Q / V
         C = 4 π ε  * R

 Here we are taking ε - the electrical permittivity in vacuum.  However, we need to take the permittivity in the material of Earth.

              C = 6 400 * 1000 / 9 * 10⁹  Farads
                   = 711.111  μ F  = 0.71111  milli Farad
Capacitances used are in the range of pico Farads and 100s of pico farads.  A  milli Farad is a high capacitance object.  If we take into account the dielectric constant of the material of Earth, then the capacitance is multiplied by the dielectric constant.  So capacitance of Earth is high.