Consider a Spherical conductor . Mark its center as o and radius r.Give some positive charge say q to charge the conductor. When we will give the charge to the conductor it will start spreading equally over its outer surface. Charge spreading does not depend upon the type of conductor used. You can take hollow as well as solid conductor. Charge spreading will be same. If the charge spreading will be uniform then the potential will be also uniform.
In the above equation Capacitance C is in farad.
We know earth is spherical. So putting the values according to the earth in the above equation.
Lets take the radius r=6400 Km.
So, it becomes 6.4 X 10 6 m.
After substituting the values :
C= Electrostatic figure 2.55 X r
= 6.4 X 10 6/9 X 10 9
=0.711 X 10 -3 farad.
So the value after calculation will be 711 uF.
It is clear from the result that the capacity of the earth is 711 microfarad. The amount 711 farad is very large. Due to such a large capacitance, earth has the ability to carry infinite amount of charge.
