n fair weather, over flat ground, there may be a downward electric field of 135
ID: 2160788 • Letter: N
Question
n fair weather, over flat ground, there may be a downward electric field of 135 N/C. (a) Assume that the Earth is a conducting sphere with charge on its surface. If the electric field just outside is 135 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 200 m above the Earth's surface, the field is only 105 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/m3Explanation / Answer
A)
electric field E = kQ/r^2
135 = 9 x 10^9 x Q/(6.4 x 10^6m)^2
Q=614400 C =614400*10^9 nC
the total charge on the Earth and the charge per unit area
=Q/area of earth
=Q/4R2
=614400*10^9/(4*(6.4 x 10^6m)^2)
=1.193 nC/m^2
B)
The field generated by the air shell must be 135 - 105 = 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 200 m^3
= 9.171 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
Q= 136533.33C
Charge density = 136533.33C /9.171 x 10^20 m^3
=1.489*10^-16 C/m^3
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