Solved (without restart) Mysql slow query log is on but not logging anything

1.First cross check /etc/my.cnf to make it permanent

slow_query_log = 1
slow_query_log_file = /var/log/mysql_slow_query.log

2.Permission of

mysql mysql  763482 Oct  6 11:43 /var/log/mysql_slow_query.log

3.Slow query logging without restart mysql

login to  mysql as root
mysql> set global slow_query_log = 1;
mysql> set global slow_query_log_file = '/var/log/mysql_slow_query.log';
mysql> flush privileges;

Cheers!!!!!!!