In the lower atmosphere of the Earth there are negative and positive ions, creat

Question

In the lower atmosphere of the Earth there are negative and positive ions, created by radioac-
tive elements in the soil and cosmic rays from space. In a certain region, the atmospheric
electric eld strength is 120 V/m, directed vertically down. Due to this eld, singly charged
positive ions, with density 620 per cm3, drift downwards and singly charged negative ions,
with density 550 per cm3, drift upwards, as shown in the gure above left. The measured
conductivity is 2:70 10??14=
m. Calculate:
(a) the ion drift speed, assumed to be the same for negative and positive ions; and
(b) the current density.

Explanation / Answer

E=120V/m; n+ = 620cm-3=620*106m-3; n- = 550cm-3 = 550*106m-3

?=2.7*10-14 (?*m)-1

? = 1/?; ?=E/J then 1/? = J/E

2.7*10-14 = J/120

J=2.7*120*10=3.24*10-12 A/m2 ===== a)


J=nevd = (n+ - n-)*e*vd

3.24*10-12 = (620-550)*10-6*1.602*10-19*vd

vd=0.289m/s

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