In fair weather, over flat ground, there may be a downward electric field of 125
ID: 2161007 • Letter: I
Question
In fair weather, over flat ground, there may be a downward electric field of 125 N/C.(a) Assume that the Earth is a conducting sphere with charge on its surface. If the electric field just outside is 125 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 220 m above the Earth's surface, the field is only 95 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
E = kQ/r^2 165 = 9 x 10^9 x Q/(6.4 x 10^6m)^2 solve for Q (7.5 x 10^5 C) nC/m^2 #nC = 7.5x 10^5 x 10^9 nC/C = 7.5 x 10^14 nC #m^2 = 4/3 Pi r^3 = 4/3 Pi (6.4x10^6)^3 = 9.23 x 10^26 m^2 divide to get nC/m^2 8.13 x 10^-13 nC/m^2 The field generated by the air shell must be 165 - 135 = 30 N/C This field comes from a charge volume of air = 4 Pi r^2 x dr = 4 x Pi x (6.4 x10^6)^2 x 210 m^3 = 9.63 x 10^20 m^3 The charge needed in the air to produce a field of 30 N/C is given by E = kQ/r^2 30 = 9 x 10^9 Q / (6.4x10^6)^2 so Q of shell is 1.37 x 10^5 C Charge density = 1.37x10^5 C /9.63 x 10^20 m^3 = work it out in C/m^3