In fair weather, over flat ground, there may be a downward electric field of 155
ID: 2162202 • Letter: I
Question
In fair weather, over flat ground, there may be a downward electric field of 155 N/C.(a) Assume that the Earth is a conducting sphere with charge on its surface. If the electric field just outside is 155 N/C pointing radially inward, calculate the total charge on the Earth and the charge per unit area.
______C
_______nC/m^2
(b) At an altitude of 280 m above the Earth's surface, the field is only 125 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/m^3
Explanation / Answer
a) E = 9x10^9 Q / R^2 , where R= 6.4 x10^6 m radius of earth from this charge on earth Q = E x R^2 / 9x10^9 , calculate this value. further, E = sigma / eo, where sigma is the charge density and eo = electric permittivity of vacuum = 8.854 x10^-12 SI units from this charge density sigma = E xeo, from this calculate the charge density. b) volume charge density rho = Q / V, where V is the volume of earth, and here subsititute values of Q and R find the volume charge density.