I don't know where I can find the answer to this question but I guess it's academic since I am a visiting research scholar here at UC Berkeley.
Based on my experience in almost the exact scenario (different University), you'll have to get a new visa, as I did for my internship(s).
There are a few programs under the J-1 visa. You are most likely in a long-term scholar or a short-term scholar program, and want to switch to an internship program.