Earth\'s lower atmosphere contains negative and positive ions that are produced

Question

Earth's lower atmosphere contains negative and positive ions that are produced by radioactive elements in the soil and cosmic rays from space. In a certain region, the atmospheric electric field strength is 109 V/m and the field is directed vertically down. This field causes singly charged positive ions, at a density of 919 cm-3, to drift downward and singly charged negative ions, at a density of 438 cm-3, to drift upward (Fig. 26-27). The measured conductivity of the air in that region is 2.88 x 10-14 (?-m)-1. Calculate the ion drift speed (in meter per second), assumed to be the same for positive and negative ions.

Explanation / Answer

J = E

= 2.88 x 10-14 (given) ; E = 109 V/m

=> J = 3.1392 - 10^-12 A/m2

Now , J =(NeVQe + NpVQp)

Qe = Qp = 1.6* 10^-19 ;

Np = 919/cm3 = 919000000/m3 ; Ne = 438000000/m3

3.1392 - 10^-12 = (919000000+438000000)VQ

=> V = (3.1392 - 10^-12)/(1.6*10^-19)*(1357000000)

=> V = 0.0144583 m/s = 1.44583 cm/s (ans)

hope this helps

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