In fair weather, over flat ground, there may be a downward electric field of 175

Question

In fair weather, over flat ground, there may be a downward electric field of 175 N/C.
(a) Assume that the Earth is a conducting sphere with charge on its surface. If the electric field just outside is 175 N/C pointing radially inward, calculate the total charge on the Earth and the charge per unit area.
C
nC/m2

(b) At an altitude of 270 m above the Earth's surface, the field is only 145 N/C. Calculate the charge density of the air (assumed constant). [Hint: See the Conceptual Example within the chapter that discusses "Field Lines for a Thin Spherical Shell".]
C/m3

Explanation / Answer

a) E = k*Q/R^2

Q = E*R/k = (175*(6.38*10^6)^2)/(9*10^9) = 124.05*10^-3 C =

791.4*10^3 micro coloumbs

sigma = Q/A = Q/4piR^2 = (791.4*10^3)/(4*3.14*(6.38*10^)^2) = 1.548 nC/m^2

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