Let us suppose that the earth had a net surface charge density of 1 electron per `m^(2)`. What would its potential be? Also what is the field just outside the earth's surface?

Explanation

Data supplied,
`sigma=1e//m^(2) =1.6 xx 10^(-19)C//m^(2), " Radius of the earth , "R=6.4 xx 10^(6)m`
Potential `V=(1)/(4pi epsi_(0) ) q/R=(1)/(4pi epsi_(0)). (sigma 4pi R^(2))/(R) =(sigma R)/(epsi_(0)) =(1.6 xx 10^(-19) xx 6.4 xx 10^(6))/(8.854 xx 10^(-12)) =0.1156V`
Field, `E=(1)/(4pi epsi_(0)).q/R^(2)=(1)/(4pi epsi_(0)) xx (sigma 4piR^(2))/(R^(2)) =(sigma)/(epsi_(0)) =(1.6 xx 10^(-19))/(8.854 xx 10^(-12))=1.81 xx 10^(-8) N//C`