On atmospheric electricity At the surface of the Earth radiu

On atmospheric electricity. At the surface of the Earth (radius 6400 km) there is an average electric field E_r -100 V/m, and a corresponding current density J_r -3.5 Times 10^-12 A/m^2 that carries electrons away from the Earth to the upper atmosphere. The potential difference between the Earth and the upper atmosphere is 400kV. What is the total current that reaches the Earth\'s surface? What power is required to maintain this current? How does it compare to the output of a power plant? Earth\'s surface charge is continually restored by lightning, which carries down negative charge from the upper atmosphere. A typical lightning stroke has a peak current of 104 A and carries 20 C. How many lightning flashes occur each second, on average, worldwide?

Solution

Earth surface area = 4*pi*(6.4e6)²   sq.m

Total current = 4*pi*(6.4e6)² *3.5e-12   = 1802 A

Power P = IV = 1802*400e+3 W = 7.208e+8 W

                                                    =720.8 MW

A super thermal power plant generates around 1000 MW

current I = dq/dt = 10^4 A

Charge tranfered = 20C

duration of the lightening current = 20/1.0e+4 = 2 ms

Total current passed to earth = 1802 A

This is equal to transfer of 1802 C charge per sec.

charge transfered per stroke = 20C

number of strokes per sec = 1802/20 = 90 approx.