Earth\'s lower atmosphere contains negative and positive ions, created by radioa

Question

Earth's lower atmosphere contains negative and positive ions, created by radioactive elements in the soil and cosmic rays from space. In a certain region, the atmospheric electric field strength is 110 V/m and the field is directed vertically down. This field causes singly changed positive ions, at a density of 630 cm^-3, to drift downward and singly changed negative ions, at a density of 570 cm^-3m, to drift upward. The measured conductivity of the air in that region is 2.70 times 10^-14 (Ohm middot m)^-1 a) Calculate the magnitude of the current density A/m^2 b) Calculate the ion drift speed, assumed to be the same for positive and negative ions. cm/s

Explanation / Answer

current density J = E*sigma

E = electric field

sigma = conductivity

for positive charge J1 = E*sigma

for negative charge J2 = E*sigma

total current density J = J1 + J2

J = 2*E*(sigma)

J = 2*110*2.7*10^-14 = 5.94*10^-12   A/m^2

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part(b)

dirft speed = vd = J/(ne)

n = 570 + 630 = 1200 /cm^3 = 1200*10^6 /m^3

vd = 5.94*10^-12/(1200*10^6 *1.6*10^-19)

vd = 0.031 m/s

vd = 3.1 m/s <<<<--------------answer

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