Use ～ところに when an event breaks in on a situation right at a critical moment — you were about to send the file, the meeting was just starting, the deal was nearly closed. It marks the incoming event as an intrusion or interruption, so the main clause almost always describes something that happens to the speaker (電話が入る、来客がある、指示が出る). In business writing it also survives in the fixed courtesy formula お忙しいところに恐れ入りますが.