A federal judge in the United States ruled Monday that Google (GOOG. O) 's maintenance of an online search monopoly is illegal, a decision that strikes at the power of big tech companies and could fundamentally change the way they do business. Judge Amit P. Mehta of the United States District Court for the District of Columbia said Google had abused its monopoly on search. The Justice Department and states sued Google, accusing it of illegally solidifying its dominance, in part by paying other companies like Apple and Samsung billions of dollars a year to have Google process search queries automatically on their smartphones and web browsers.