It depends on the diameter of the "earth". If it is exactly the same size as Earth, then a 7,917.5 mile long wire would be required.
"The strongest current was found around the galaxy 3C303, whose core is the origin of a massive matter jet." (POPULAR SCIENCE, The Strongest Electrical Current)
This galaxy is admitting 1018 amps. This equals one TRILLION bolts of lighting.
The Earth's magnetic field at its surface ranges from 35 to 65 microteslas.
I think the correct answer from the choices listed above is option 4. I think it is the process of convection that is responsible for the greatest loss of energy from Earth’s surface into space on a clear night. Convection happens when a mass which contains heat energy is in motion. This happens in wind blowing, oceanic currents and other naturally occurring fluid flows.<span />