SAN JOSE, California — The U.S. Justice Department on Tuesday sharply cut its demand for Google Inc. customer data and a U.S. judge signaled he intended to require the search company to hand over some records, potentially opening the door to compromise in a test case for Web privacy. U.S. District Court Judge James Ware told a hearing he would make a decision that weighed the government’s need to gather data against Google’s needs as a private company to defend its trade secrets. Ware added that he was concerned about creating the perception that Google’s users’ privacy could be undermined, but he reacted positively to the reduced request by the government, which is seeking data for a study on Internet child pornography. “It is my intent to grant some relief to the government,” said Ware of the U.S. District Court for the Northern District of California, adding that he expected to make a decision “very quickly.” Shares of Google’s (GOOG) stock rose $14.10, or 4.2 percent, to close at $351.16. The government on Tuesday reduced the number of Google searches it wanted data on to just 50,000 Web addresses and roughly 5,000 search terms from […]