Um, may I suggest you do not change preference settings as this often leads to creating a mess with broken links.
iTunes: How to move [or copy] your music to a new computer [or another drive] - http://support.apple.com/kb/HT4527
Quick answer if you let iTunes manage your music: Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive. Start iTunes with the option (shift on Windows) key held down and guide it to the new location of the library.
Do not confuse moving your whole folder and library with moving just media files as in:
iTunes for Mac: Moving your iTunes Media folder - http://support.apple.com/kb/HT1449
Note that the external will always have to be turned on before starting iTunes. If you forget to do that, iTunes will revert to the default library location on the internal drive. no problem. Just start iTunes again with the option key held down and point it to the external again.