suppose that earth has a surface charge density of 1 electron/metre2.Calculate earth potential and electric field just outside earth surface.Radius of earth 6400 km

According to Gauss's theorem of electric flux vector,     E.ds=qε0We are given  σ=1e/m2, R=6.4×106mSo     4πR2=4×3.14×6.4×106×6.4×106=514.46×1012Therefore charge on the surface area of the earth is given by;          q=σ×4πR2=1 electronic charge×514.46×1012or          q=1.6×10-19×514.46×1012=823.136×10-7CTherefore        E=σε0=1.6×10-198.85×10-12=1.81×10-13N/CThe earth's potential V=14πε0×qR=9×109×823.136×10-76.4×106or              V=74.076.4×10-2=0.116Volt

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