If you need to back up a database using SQL query in SQL Server. You can use the built-in function called 'BACKUP DATABASE'. In order to be able to successfully run the query. You need to ensure that the query is run under db_owner of the database (database owner) and also the location of the backup folder needs to have access permission.
Here is the error message if you try to back up the database into a drive location that you do not have access.
Here is the TSQL query to do a full backup of a database.
BACKUP DATABASE [mydatabasename] TO DISK = 'C:/mydatabasename.bak'