http://admission.universityofcalifornia.edu/transfer/preparing-admission/minimum-requirements/index.html indicates that the seven course pattern including four courses from at least two of the categories arts/humanities, social/behavioral sciences, physical/biological sciences is a requirement for transfer admission. Presumably, you took physics courses for the EECS major. If you did not meet this pattern, then you may have to complete it and try again next year.
http://www.universityofcalifornia.edu/infocenter/transfers-major indicates that, for 2015, UCB EECS transfer admissions had an 8% admit rate (91 out of 1,116 applicants), with the 25th and 75th percentile GPAs of 3.88 and 4.00 respectively for admitted students. The essays are presumably quite important with so many applicants pressed up against the maximum GPA.