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 \(u_{0}^{-}=1.91 \mathrm{~cm}^{2} /(\mathrm{V} \cdot \mathrm{s})\)