[W]e know that to produce 1 coulomb of charge by the ionization of air requires an energy absorption of 33.85 joules.There you go. You have a little pocket of air. An x-ray passes by and excites it, transferring 33.85 Joules of energy to it and poof! You have created 1 Coulomb of charge in that little pocket of air. If you have an electrometer nearby you can detect it.
See Johns and Cunningham (1983), The Physics of Radiology, 4th edition, p. 235.
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