They are not sentences. They are just phrases, so don't need capitalization and periods.
Both are correct, but B is more likely to be used.
2006Why is B better to use? It's not necessarily better, but it probably is more commonly used.
"under the spell of the music" refers to specific music, the music he is listening to at that time.
He won't talk to you now; he is under the spell of the music.
"under the spell of music" refers to music in general.
He spends a lot of his time under the spell of music.