SQL Server: How to move a database file

I recently had to move the log file of a SQL Server database. Initially I thought it might be a simple alter database command, as in How to Change a Database File, but that does not work out:

-- Note: this will not work
alter database MyDatabase
modify file (name='MyDatabase_Log',
filename='c:\Program Files\Microsoft SQL Server\MSSQL\Data_log\MyDatabase_Log.LDF')
go
Msg 5037, Level 16, State 1, Server MYSERVER, Line 1
MODIFY FILE failed. Do not specify physical name.

I found the answer in the SQL Server 2000 Administrator's Pocket Consultant: you have to detach the database, move the file using Windows, and then reattach the database, specifying where the files have gone:

-- Put the database in single user mode
use master
exec sp_dboption MyDatabase, 'single user', true
go

-- Find out where the database files are located
exec sp_helpdb MyDatabase
...
C:\Program Files\Microsoft SQL Server\MSSQL\data\MyDatabase_Data.MDF
C:\Program Files\Microsoft SQL Server\MSSQL\data\MyDatabase_Log.LDF

-- Detach the database
exec sp_detach_db 'MyDatabase', 'true'
go

-- After this, you will need to move the files to their new locations using Windows

-- Reattach the database, specifying where the files are now located
exec sp_attach_db 'MyDatabase',
'C:\Program Files\Microsoft SQL Server\MSSQL\data\MyDatabase_Data.MDF',
'C:\Program Files\Microsoft SQL Server\MSSQL\data_log\MyDatabase_Log.LDF'
go