An EMB145 engine failed after takeoff on the climb out at 11;000 FT. An emergency was declared with a return to land.

Narrative

Departed as reposition flight. After climbing through 11000 FT the aircraft yawed to the left. Immediately; I grabbed the controls and looked at the EICAS. The N1 indications showed indications of an engine failure. Immediately thereafter the Master Caution ENG 2 OUT appeared. I asked the First Officer to request 12000 FT and a heading. After ATC replied I asked him to declared the emergency and then request the heading and altitude. We ran the appropriate checklists. At the point in time when we were to consider restarting the engine; the APU showed a rapid increase in temperature and failed. We received an APU FAIL message. At that point we decided not to restart the number 2 engine and land immediately. After completing all checklist items and performing all required duties; we then notified ATC that we were ready to commence an approach. Upon landing we received an ENG 2 NO DISP warning. I asked the emergency vehicles that had escorted us if it was safe to proceed. After getting the thumbs up; we taxied to the hard stand and wrote up the discrepancies.