slow_query_log_file

slow_query_log=1
slow_query_log_file="/var/log/mysqld2.log"
long_query_time = 2

I set these 3 variables in my.cnf, and phpmyadmin confirms that they are set. Phpmyadmin states that there have been slow queries, yet the log file remains empty.

Do I need to chmod or chown the log file to anything special?

Did you restart the server after changing the my.cnf file?

Yes.