Problem 3.212

The air between two parallel plates separated by a distance $d=20 \mathrm{~mm}$ is ionized by $X$ -ray radiation. Each plate has an area $S=500 \mathrm{~cm}^{2} .$ Find the concentration of positive ions if at a voltage $V=100 \mathrm{~V}$ a current $I=3.0 \mu \mathrm{A}$ flows between the plates, which is well below the saturation current. The air ion mobilities are $u_{\mathrm{n}}^{+}$ $=1.37 \mathrm{~cm}^{2} /(\mathrm{V} \cdot \mathrm{s})$ and $u_{0}^{-}=1.91 \mathrm{~cm}^{2} /(\mathrm{V} \cdot \mathrm{s})$